Define Tautology and Contradiction. Construct the truth table for the compound statement(~ ∧ ( ∨ )) ⇒∼ (∼ ). What would you conclude from the truth table?
(please solve that)
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A compound proposition that is always true for all possible truth values of the propositions is called a tautology. A compound proposition that is always false is called a contradiction. A proposition that is neither a tautology nor contradiction is called a contingency. Example: p ∨ ¬p is a tautology.
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Answer
The given statement pattern is
(p∧∼q)↔(p→q)
Truth Table
p q ∼q p∧∼q p→q (p∧∼q)↔(p→q)
T T F F T F
T F T T F F
F T F F T F
F F T F T F
All the entries in the last column of the above truth table are F.
∴(p∧∼q)↔(p→q) is a contradiction
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