Question
Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency.
Solution
No of rows = 2n=23 =8
No. of columns = m+ n=3+3= 6
| p | q | r | p ∧ q | p ∧ r | (p ∧ q) ∨ (p ∧ r) |
| T | T | T | T | T | T |
| T | T | F | T | F | T |
| T | F | T | F | T | T |
| T | F | F | F | F | F |
| F | T | T | F | F | F |
| F | T | F | F | F | F |
| F | F | T | F | F | F |
| F | F | F | F | F | F |
In the last column, the truth values of the statement is neither all T nor all F. Hence, it is neither a tautology nor a contradiction i.e. it is a contingency.
Is there an error in this question or solution?
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Solution Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency. Concept: Mathematical Logic - Truth Value of Statement in Logic.
