means "if A is true then B is true." contrapositive is "if B is not true then A is not true."

to see why the contrapositive is equivalent assume the contrapositive statement holds. that is "if B is not true then A is not true.". we shall show that this implies "if A is true then B is true." use contradiction method. so further assume that there exists a case when A is true but B is not true. BUT WE STARTED WITH if B is not true then A is not true(this was the contrapositive statement ). so there is a contradiction between the blue and the green statements.

hence "if B is not true then A is not true" leads us to "if A is true then B is true."

now it remains to show that "if A is true then B is true" leads us to "if B is not true then A is not true."

if this is done then the equivalence of the contapositive and the original will be established. can you try and do it?