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Question

# Statement - 1: ∼(p↔∼q) is equivalent to p↔q. Statement - 2: ∼(p↔∼q) is a tautology.

A
Statement - 1 is true, Statement - 2 is true;
Statement - 2 is not a correct explanation for statement - 1.
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B
Statement - 1 is true, Statement - 2 is false.
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C
Statement - 1 is false, Statement - 2 is true.
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D
Statement - 1 is true, Statement - 2 is true,
Statement - 2 is a correct explanation for statement - 1.
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Solution

## The correct option is B Statement - 1 is true, Statement - 2 is false.The truth table for the logical statements, involved in statement 1, is as follows: pq∼qp↔∼q∼(p↔∼q)p↔qTTFFTTTFTTFFFTFTFFFFTFTT We observe the columns for ∼(p↔∼q) and p↔q are identical, therefore ∼(p↔∼q) is equivalent to p↔q But ∼(p↔∼q) is not a tautology as all entries in its column are not T. ∴ Statement - 1 is true but statement - 2 is false.

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