If p → ( ¬p ∨ q) is false, then the truth values of p and q are respectively T, F.Group startsTrue or FalseTrue, unselectedFalse, unselected
Question
If p → ( ¬p ∨ q) is false, then the truth values of p and q are respectively T, F.
Group starts
True or False
True, unselected
False, unselected
Solution
To determine the truth values of p and q in the given statement, let's analyze the expression p → (¬p ∨ q) when it is false.
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The expression p → (¬p ∨ q) is false when the antecedent (p) is true and the consequent (¬p ∨ q) is false.
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Since the antecedent (p) is true, we can conclude that p is true.
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Now, let's analyze the consequent (¬p ∨ q). Since the entire expression is false, the consequent must also be false.
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The expression ¬p ∨ q is false when both ¬p and q are false.
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Since the consequent (¬p ∨ q) is false, we can conclude that both ¬p and q are false.
Therefore, the truth values of p and q in the given statement are p = true and q = false.
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