Question:
Among the given statements below
(a) \( \neg p \vee (\neg p \vee q) \)
(b) \( \neg q \wedge (\neg p \vee \neg q) \)
(c) \( (\neg p \vee \neg q) \wedge (p \vee \neg q) \)
(d) \( (\neg p \vee \neg q) \vee (p \vee \neg q) \)
.............. is a tautology.
Among the given statements below
(a) \( \neg p \vee (\neg p \vee q) \)
(b) \( \neg q \wedge (\neg p \vee \neg q) \)
(c) \( (\neg p \vee \neg q) \wedge (p \vee \neg q) \)
(d) \( (\neg p \vee \neg q) \vee (p \vee \neg q) \)
.............. is a tautology.
Show Hint
To determine if a logical statement is a tautology, construct the truth table for the expression and check if it evaluates to true for all possible combinations of truth values.
Updated On: Mar 28, 2026
- (b)
- (a)
- (c)
- (d)
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The Correct Option is D
Solution and Explanation
Step 1: Analyze each logical statement.
We need to check whether any of the given logical statements result in a tautology. A tautology is a statement that is always true, regardless of the truth values of its components.
Step 2: Check the truth tables for each statement.
We will construct the truth tables for the given options and determine if any of the statements are always true. For statement (d): \[ (\neg p \vee \neg q) \vee (p \vee \neg q) \] This expression simplifies to: \[ (\neg p \vee \neg q) \vee (p \vee \neg q) = \text{true} \] This is a tautology because it evaluates to true for all possible truth values of \( p \) and \( q \).
Step 3: Conclusion.
Thus, the correct answer is (d), which is a tautology.
We need to check whether any of the given logical statements result in a tautology. A tautology is a statement that is always true, regardless of the truth values of its components.
Step 2: Check the truth tables for each statement.
We will construct the truth tables for the given options and determine if any of the statements are always true. For statement (d): \[ (\neg p \vee \neg q) \vee (p \vee \neg q) \] This expression simplifies to: \[ (\neg p \vee \neg q) \vee (p \vee \neg q) = \text{true} \] This is a tautology because it evaluates to true for all possible truth values of \( p \) and \( q \).
Step 3: Conclusion.
Thus, the correct answer is (d), which is a tautology.
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