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

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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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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Given the following statement if p then q .....(1) is true then there are three possibilities if ~p then ~q ....(2) is the inverse of the statement, which is not always true when (1) is true. if ~q then ~p .....(3) is the contrapositive, it is equivalent to statement (1), so whenever (1) is true, then (3) is true. if q then p ....(4) is the converse, and is not always true even when (1) is true. Based on the above hints, you should be able to figure out the answer. To give an example: If bananas cost $0.50 each, I will buy one .....(A).... assume that this is true. If bananas don't cost $0.50 each, I won't buy any. ........ (B) ....... it may cost $2.00 each , in which case I don't buy. ........it may cost $0.10 each, in which case I \(might\) buy one. So if (A) is true, (B) may or may not be true, in other words, (B) is not always true.

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