Question 1181633: Find the truth value of the following: Show the solution.
2. ¬(r→s)∨[(p∧¬q)∨¬s]
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's determine the truth value of ¬(r→s)∨[(p∧¬q)∨¬s] using a truth table. Since there are four variables (p, q, r, s), there are 2⁴ = 16 possible combinations of truth values.
Here's the truth table:
| p | q | r | s | ¬q | ¬s | r→s | ¬(r→s) | p∧¬q | (p∧¬q)∨¬s | ¬(r→s)∨[(p∧¬q)∨¬s] |
|---|---|---|---|----|----|-----|--------|------|----------|-----------------------|
| T | T | T | T | F | F | T | F | F | F | F |
| T | T | T | F | F | T | F | T | F | T | T |
| T | T | F | T | F | F | T | F | F | F | F |
| T | T | F | F | F | T | T | F | F | T | T |
| T | F | T | T | T | F | T | F | T | T | T |
| T | F | T | F | T | T | F | T | T | T | T |
| T | F | F | T | T | F | T | F | T | T | T |
| T | F | F | F | T | T | T | F | T | T | T |
| F | T | T | T | F | F | T | F | F | F | F |
| F | T | T | F | F | T | F | T | F | T | T |
| F | T | F | T | F | F | T | F | F | F | F |
| F | T | F | F | F | T | T | F | F | T | T |
| F | F | T | T | T | F | T | F | F | F | F |
| F | F | T | F | T | T | F | T | F | T | T |
| F | F | F | T | T | F | T | F | F | F | F |
| F | F | F | F | T | T | T | F | F | T | T |
Since the final column has both T and F values, the given statement is a **contingency**. Its truth value depends on the specific truth values of p, q, r, and s.
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