A => B

“A implies B”

“If A then B”

“A therefore B”

Example:

If A means “It is raining outside” and B means “my lawn is wet” then A => B because rain makes the lawn wet.  We do not have the opposite statement though ( B does not imply A) because a wet lawn could be caused by other things than rain, such as a water sprinkler system, or it could have rained earlier in the day, or your pet could have whizzed on the lawn.

A <=B

“A is implied by B”

If it happens that A => B and B => A then both of these statements can be expressed as a single statement:

A <=> B

read “A if and only if B” or abbreviate the if and only if part with iff:

“A iff B”

Since A implies B and B implies A, this means that statements A and B are logically equivalent (A is true only when B is true and B is true only when A is true).