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When we learn about if-else statements, 2

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comparison and equality operators 3

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and Boolean values. 4

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We also need to learn about logic. 5

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And in particular about Boolean logic. 6

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So let's do that in this video. 7

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So basically Boolean logic 8

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is a branch of computer science, 9

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which uses true and false values 10

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to solve complex logical problems. 11

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And in order to do that, 12

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it uses several logical operators 13

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to combine true and false values. 14

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So much like we use arithmetic operators, 15

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to combine numeric values. 16

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Now we're only going to scratch the surface here 17

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and talk about the most basic logical operators, 18

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which are the AND, OR, and NOT operators. 19

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And note that Boolean logic 20

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is actually not specific to JavaScript. 21

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This is all true for all programming. 22

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But anyway, 23

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let's now understand how these operators work 24

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and use an example to illustrate it. 25

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So here we have two Boolean variables 26

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that can either be true or false. 27

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So A is that Sarah has a driver's license 28

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and B is that Sarah has good vision. 29

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So both of these are of course conditions, 30

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that can be true or false 31

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because Sarah could have no driver's license 32

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and she could have no good vision, 33

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right. 34

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And of course on the other hand, 35

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she could also have a driver's license 36

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and could have good vision. 37

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Now using the AND operator like A aND B, 38

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we can combine these two Boolean variables 39

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like Sarah has a driver's license and good vision. 40

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Okay. 41

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But now what will be the result of this operation? 42

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Well for that, 43

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we use a so-called truth table, 44

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which looks something like this. 45

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Here we have to two possible values 46

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for each of the variables, 47

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A AND B, 48

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which gives us four possible combinations of results. 49

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And so then all we have to do 50

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is to plug in the value of our variables, 51

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and to get a result of the AND operation 52

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from this table. 53

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So what we can see from this table 54

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is that only if both A and B are true, 55

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the result of the operation will be true as well. 56

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And that makes sense, right! 57

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After all, 58

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it's called the AND operator. 59

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And so again, 60

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what the AND operator does 61

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is to return true 62

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only if both A AND B are true. 63

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In all other situations, 64

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if either A or B are false, 65

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then A AND B will also be false. 66

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And we can also generalize this to more operands. 67

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So to more than just two values, 68

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we could do A AND B AND C, 69

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and results would be true 70

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only if all of them are true. 71

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And if one of them is false, 72

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then the result is immediately false as well. 73

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Now I know that all of this, 74

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might look a little bit confusing, 75

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but don't worry We will have an example, 76

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a little bit later in this lecture, 77

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and we will also use this in practice 78

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and the next one. 79

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And after some practice, 80

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you will internalize all of this 81

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and you won't even need any truth tables. 82

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Now moving on, 83

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on the other hand, 84

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we also have the OR operator, 85

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which kind of works in the opposite way. 86

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So with our current example, 87

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we could use the OR operator 88

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to determine whether Sarah 89

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has a driver's license or good vision. 90

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And just by thinking about this, 91

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we can already intuitively imagine 92

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that the OR operator will be true 93

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if just one of the variables is true. 94

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And in fact, 95

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a look at the truth table confirms exactly that. 96

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So unlike the AND operator and the OR operator, 97

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even if one of the variables is false, 98

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the outcome will still be true. 99

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Or in other words, 100

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if either A OR B is true, 101

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then the OR operation becomes true as well. 102

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And that's why it's called the OR operator. 103

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And once more, 104

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if we have multiple variables, 105

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it's enough for one of them to be true, 106

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to make the whole operation become true as well. 107

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Okay, I hope this makes sense. 108

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And once again, 109

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I can assure you 110

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that it will make sense 111

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once we start using this in practice. 112

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Anyway, 113

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we finally also have the NOT operator, 114

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which is a lot simpler 115

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because it doesn't combine multiple values. 116

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Instead, 117

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the NOT operator acts on only one Boolean value 118

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and it basically just inverts it. 119

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So if A is true, 120

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it will become false. 121

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And if it's false, 122

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then NOT A will become true, 123

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simple as that. 124

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And that's basically 125

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how these three most important logical operators work. 126

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But of course, 127

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the best way to understand it 128

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is to use a more practical example. 129

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So let's go again back 130

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to using the age, 131

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and this time we set it to 16. 132

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And then we have, 133

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our two Boolean variables. 134

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The first one is age is greater or equal 20. 135

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And the second one is age is less than 30. 136

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So let's determine the value of each of them. 137

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So if age is 16, 138

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then age is greater or equal to any 139

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must be false. 140

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Right! 141

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And of course it is, 142

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and age is less than 30 is true 143

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because 16 obviously is less than 30. 144

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Okay. 145

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So that's the baseline basically, 146

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and now we will start to combine 147

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these variables A and B 148

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using some logical operators. 149

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So the first exercise 150

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is the NOT operator. 151

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So NOT A, 152

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and we know right now that A is false, right? 153

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So the result of NOT A, 154

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as we just learned is true, 155

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because all it does 156

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is to invert the logical value of the variable. 157

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Next one we have A AND B, 158

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now we already know that A is false and B is true. 159

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So I'm just putting these values here again, 160

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to make it a bit easier to follow. 161

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Okay. 162

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So we have basically false and true. 163

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So from a look at our truth table here 164

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at the right side, 165

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we can easily determine 166

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that the result of this must be false. 167

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And so that's exactly 168

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what we learned before. 169

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So when we have the AND operator, 170

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it's enough for one of the operands to be false, 171

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to make the result of the operation also false. 172

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Now we have A OR B, 173

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and so let's check out the truth table in this case. 174

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And so in this case, 175

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we actually get true. 176

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And so this shows that it is enough 177

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for one variable to be true 178

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for the whole expression to be true as well. 179

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Next up let's check NOT A AND B. 180

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And we already know 181

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that NOT A is true and B is true. 182

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And so at this time for the first time, 183

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we are combining multiple operators here 184

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and yeah we already know that true and true 185

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will of course be true as well. 186

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And now another one combining two operators, 187

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so A OR NOT B. 188

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And just as a side note, 189

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the NOT operator actually has proceedings 190

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over the OR and AND operators. 191

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So basically the values are inverted first 192

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and only then they are combined using AND or OR. 193

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So we know that A is false and B is true. 194

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So NOT B must be false, right 195

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then false OR false is also false. 196

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And actually that's the only way in which 197

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the OR operator can be false. 198

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If all of them are false basically. 199

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So I hope that made sense to you. 200

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And so in the next lecture, 201

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we will actually use these operators in a code. 202

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And then it will make even more sense to you. 203

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So by then, 204

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we probably won't even need the truth tables anymore, 205

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because it will become quite intuitive 206

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how both of these operators actually work. 207

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But anyway, let's now move on 208

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and I see you in the next video.