Maharashtra State BoardHSC Arts 12th Board Exam
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Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.[(p → q) ∧ q] → p - Mathematics and Statistics

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Sum

Examine whether the following logical statement pattern is a tautology, contradiction, or contingency.
[(p → q) ∧ q] → p

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Solution

Consider the statement pattern : [ ( p → q ) ∧ q ] → p
No. of rows = 2n = 2 × 2 = 4
No. of column = m + n = 3 + 2 = 5
Thus the truth table of the given logical statement :
[(p → q) ∧ q] → p

p q p → q (p → q) ∧ q [(p → q) ∧ q] → p
T T T T T
T F F F T
F T T T F
F F T F T

From the above truth table we can say that given logical statement: [(p → q) ∧ q] → p is contingency.

Concept: Statement Patterns and Logical Equivalence
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