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Question:

Consider the following statements: Statement I: (p∧¬q)∧(¬p∧q) is a fallacy. Statement II: (p→q)↔(¬q→¬p) is a tautology. Statement I is True; Statement II is true; Statement II is not a correct explanation for Statement I. Statement I is True; Statement II is False. Statement I is False; Statement II is True. Statement I is True; Statement II is True; Statement II is a correct explanation for Statement I.

Statement I is True; Statement II is true; Statement II is not a correct explanation for Statement I

Statement I is True; Statement II is False

Statement I is False; Statement II is True

Statement I is True; Statement II is True; Statement II is a correct explanation for Statement I

Solution:

STATEMENT 1
Truth table for (p∧¬q)∧(¬p∧q).
p q ¬p ¬q (p∧¬q) (¬p∧q) (p∧¬q)∧(¬p∧q)
T T F F F F F
T F F T T F F
F T T F F F F
F F T T F F F
Therefore, (p∧¬q)∧(¬p∧q) is a FALLACY.
Statement 1 is TRUE.
STATEMENT 2
Truth table for (p→q)↔(¬q→¬p).
p q ¬p ¬q p→q ¬q→¬p (p→q)↔(¬q→¬p)
T T F F T T T
T F F T F F F
F T T F T T T
F F T T T T T
Therefore, statement 2 is a TAUTOLOGY.
Statement 2 is TRUE.
Also, Statement 2 is not correct explanation of Statement 1.
Therefore, option (A) is the correct answer.