the contrapositive of 'not A => not B' is 'A=>B', where.... (Elementary Algebra)

Question

the contrapositive of 'not A => not B' is 'A=>B', where A and B are 2 statements.... State true or false and give a proof supporting your answer.

Answer 1

Example: Let A="this is not red" and B="this is blue". Not A is "this is red" and not B is "this is not blue". "This is red" implies "this is not blue". So not A ⇒ not B; does A imply B? "This is not red" implies "this is blue" is false, because "not red" covers many colours, not just blue. So the proposition is generally false. It would only be true if red and blue were the only colours and "this" was constrained to be red or blue.