Let p, q, and r have truth values F, F, T, respectively. Then determine the truth value of the following:

1. p ∧ q
Since both p and q are false, the conjunction of p and q is false.
Answer: F

2. p ∨ q
Since at least one of p and q is true, the disjunction of p and q is true.
Answer: T

3. ¬r
The negation of r is false.
Answer: F

4. p ∧ ¬r
Since p is false and ¬r is false, the conjunction of p and ¬r is false.
Answer: F

5. (p ∨ q) ∧ r
Since p ∨ q is true and r is true, the conjunction of (p ∨ q) and r is true.
Answer: T

~(p → q → r)

Truth table for ~(p → q → r):

| p | q | r | p → q | q → r | p → q → r | ~(p → q → r) |
|---|---|---|---|---|---|---|
| F | F | T | T | T | T | F |
| F | F | F | T | F | F | T |
| F | T | T | T | T | T | F |
| F | T | F | T | F | F | T |
| T | F | T | F | T | F | T |
| T | F | F | F | F | F | T |
| T | T | T | T | T | T | F |
| T | T | F | T | F | F | T |

Therefore, the truth value of ~(p → q → r) is F.