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Question
Examine whether the statement pattern (p ∧ q) and (∼ p ∨ ∼ q) is a tautology or contradiction or contingency.
Sum
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Solution
We need to examine the compound statement:
(p ∧ q) ∧ (∼ p ∨ ∼ q)
Step 1: Understand the statement
p ∧ q Both p and q are true.
∼ p ∨ ∼ q At least one of p or q is false.
These two parts contradict each other.
Step 2: Truth Table
| p | q | p ∧ q | ∼ p | ∼ q | ∼ p ∨ ∼ q | Whole Statement |
| T | T | T | F | F | F | F |
| T | F | F | F | T | T | F |
| F | T | F | T | F | T | F |
| F | F | F | T | T | T | F |
Step 3: Conclusion
The final column is false in all cases.
The statement is a contradiction.
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