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Which of the following are true statements based on the given conditional statements?

A) Conditional and Converse are true.
B) Conditional and Inverse are true.
C) Conditional and Contrapositive are true.
D) Conditional and Converse are false.

1 Answer

3 votes

Final answer:

The true statements based on the given conditional statements are the conditional and its contrapositive, making option C the correct answer.

Step-by-step explanation:

The truth of a conditional statement and its related forms—converse, inverse, and contrapositive—depends on the logic of their constructions. The conditional is an if-then statement (e.g., If X, then Y). The converse switches the hypothesis and conclusion (If Y, then X). The inverse negates both the hypothesis and conclusion (If not X, then not Y). The contrapositive negates and switches the hypothesis and conclusion (If not Y, then not X).

Of these, the contrapositive is always logically equivalent to the conditional: if the conditional is true, so is the contrapositive.

With that said, the answer to the question 'Which of the following are true statements based on the given conditional statements?' would be C) Conditional and Contrapositive are true. This is because a true conditional statement will always have a true contrapositive.

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User Shreyos Adikari
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