Answer to Question #317909 in Discrete Mathematics for Donnel

Question

C. Let p and q be proposition

p: 4 is a rational number

q: √3 is an irrational number

Express each of these proposition as an English sentences:

1. ~p
2. p∨ q
3. p ∧ q
4. p → q
5. p ↔ q

Answer 1

1: 4 is not a rational number

2: 4 is a rational number or $\sqrt{3}$ is an irrational number

3: 4 is a rational number and $\sqrt{3}$ is an irrational number

4: if 4 is a rational number then $\sqrt{3}$ is an irrational number

5: 4 is a rational number if and only if $\sqrt{3}$ is an irrational number