Question

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

Answer 1

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.