Question

Let A and B be two propositions. Explain the differences
between the constructs A <-> B and A <=> B

Answer 1

you have the following posibilities:
A -> B means:
if A is true then B is true
but if B is true that does not necesarilly mean that A is true.
Example if it rains I will use my umbrella, always. But I can use my umbrella even if it's not raining if I feel like it.

A <=> B
means that if A is true, B is true as well
and if A is false, B is false as well.
So either A and B are both true, or both false.