Question 1167126: Complete the following Truth Table
p q r ~(p ∨ ~q) ∨ ~r
T T T (a)
T T F (b)
T F T (c)
T F F (d)
F T T (e)
F T F (f)
F F T (g)
F F F (h) Answer by CPhill(1987) (Show Source):
You can put this solution on YOUR website! You need to evaluate the compound proposition $\sim(p \lor \sim q) \lor \sim r$ for each row. The symbol $\sim$ means NOT (negation), $\lor$ means OR (disjunction).
| p | q | r | $\sim q$ | $p \lor \sim q$ | $\sim(p \lor \sim q)$ | $\sim r$ | $\sim(p \lor \sim q) \lor \sim r$ | Result |
| :-: | :-: | :-: | :-: | :-: | :-: | :-: | :-: | :---: |
| T | T | T | F | T | F | F | F $\lor$ F = F | **(a) F** |
| T | T | F | F | T | F | T | F $\lor$ T = T | **(b) T** |
| T | F | T | T | T | F | F | F $\lor$ F = F | **(c) F** |
| T | F | F | T | T | F | T | F $\lor$ T = T | **(d) T** |
| F | T | T | F | F | T | F | T $\lor$ F = T | **(e) T** |
| F | T | F | F | F | T | T | T $\lor$ T = T | **(f) T** |
| F | F | T | T | T | F | F | F $\lor$ F = F | **(g) F** |
| F | F | F | T | T | F | T | F $\lor$ T = T | **(h) T** |
***
### Final Answers
| Letter | Result |
| :---: | :---: |
| **(a)** | **F** |
| **(b)** | **T** |
| **(c)** | **F** |
| **(d)** | **T** |
| **(e)** | **T** |
| **(f)** | **T** |
| **(g)** | **F** |
| **(h)** | **T** |
