QuestionAugust 8, 2025

True or false? If you took a true "If-then"statement and inserted a not in each clause, the new statement would also be true. A. True B. False

True or false? If you took a true "If-then"statement and inserted a not in each clause, the new statement would also be true. A. True B. False
True or false? If you took a true "If-then"statement and inserted a not in each
clause, the new statement would also be true.
A. True
B. False

Solution
4.5(93 votes)

Answer

B. False Explanation 1. Understand the Original Statement A true "If-then" statement is of the form "If P, then Q" (P → Q). 2. Apply Negation to Each Clause The negated statement becomes "If not P, then not Q" (~P → ~Q). 3. Analyze the Logical Equivalence The original and negated statements are not logically equivalent. The negation of an implication is not another implication but rather "P and not Q" (P ∧ ~Q).

Explanation

1. Understand the Original Statement<br /> A true "If-then" statement is of the form "If P, then Q" (P → Q).<br />2. Apply Negation to Each Clause<br /> The negated statement becomes "If not P, then not Q" (~P → ~Q).<br />3. Analyze the Logical Equivalence<br /> The original and negated statements are not logically equivalent. The negation of an implication is not another implication but rather "P and not Q" (P ∧ ~Q).
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