Discrete Math for CS LECTURE 2 Propositions Truth

Discrete Math for CS LECTURE 2 • Propositions • Truth tables • Quantifiers 5/18/2021

Propositions A proposition is a statement that is either true or false. 5/18/2021 L 2. 2

Joining propositions • 5/18/2021 L 2. 3

Truth tables 5/18/2021 L 2. 4

I-clicker problem (frequency: BC) • A. 5/18/2021 B. C. L 2. 5

Most common connective • 5/18/2021 L 2. 6

Logical equivalence • 5/18/2021 L 2. 7

Iff • Ex. : Today is Monday iff tomorrow is Tuesday. 5/18/2021 L 2. 8

Operations on implications • If you were born in the US then you are a US citizen. If you are a US citizen then you were born in the US. If you are not a US citizen, you weren’t born in the US. 5/18/2021 L 2. 9

Operations on implications • 5/18/2021 L 2. 10

I-clicker problem (frequency: BC) If the old lady swallowed a fly, she swallowed a spider. If she did not swallow a bird, she did not swallow a spider. She swallowed a cat, provided that she swallowed a bird. Then which implication must hold? A. If she swallowed a cat then she swallowed a spider. B. If she swallowed a cat then she swallowed a fly. C. She will die. D. If she swallowed a fly then she swallowed a cat. E. If she swallowed a fly then she swallowed a horse. 5/18/2021 L 2. 11

Common logical equivalences • 5/18/2021 L 2. 12

Propositions with quantifiers • 5/18/2021 L 2. 13

Summary • 5/18/2021 L 2. 14