Connectives and Truth Values

∧

∨

→

↔

A = Samir is tall

B = Tamer is short

Samir is tall and Tamer is short

a) A ∧ B         b) A ∨ B         c) A → B           d) A ¬ B

1. If A is true and B is false, what truth value would you assign to A ∧ B?
2. If A is false and B is true, what truth value would you assign to A ∧ B?
3. If A and B are both false, what truth value would you assign to A ∧ B?

Choose from the following options

1. A ¬ B
2. A ∧ B
3. A → B
4. A ∨ B

Your friend promised that if he/she passes the exam, then he/she will go to Friday soccer game. If your friend passes the test and goes to watch the soccer game, the remark was true. If your friend passes the test but doesn’t go to watch the soccer game, the remark was false. If your friend doesn’t pass the test, then—whether he/she goes to watch the soccer game or not—you could not claim that the remark was false. You would probably want to give the benefit of the doubt and say that the statement was true. By convention, A → B is considered true if A is false, regardless of the truth value of B.

Choose from the following options which are ordered from top to bottom

If A → B is true, then A must be true

Given A → B

while the truth of A implies the truth of B, the truth of B does not imply the truth of A

A ↔ B

1. (A → B) ∧ (B → A)
2. (A ∧ B) ∨ (B ∧ A)
3. (A ∨ B) ∧ (B ∨ A)
4. (A ¬ B) ∨ (B ¬ A)

which one of the following options which are ordered top down

A )) ∧ ∧ → BC

1. ∧ ∨ 
2. '
3. →  
4. connectives within parentheses, innermost parentheses first
5. ↔ 

((A ∨ B) ∧ C) → (B ∨ C')

1. ∧
2. ∨
3. →
4. '
5. Parentheses

1. 2 * n
2. 2 + n
3. n²
4. 2ⁿ