I simply cannot remember which is normalized and which is denormalized. I cannot do coordinate transforms — I consider myself “spatially impared”. And I can never remember the truth table for *implies*.

“*p* implies *q*” or “*p* only if *q*” has the following truth table:

p|q|p->q---+---+-------- T | T | T T | F | F F | T | T F | F | T

where *p* and *q* are propositions.

It is logically equivalent to say:

*p*implies*q**q*is a necessary condition for*p**p*is a sufficient condition of*q*- in order that
*p*be true it is necessary that*q*be true - if
*p*is true then*q*is true

For example:

If a person is a father then a person is male.

This statement is of the form *p* -> *q* where:

*p*: A person is a father*q*: A person is male

It is *necessary* for a person to be male to be a father. Being a father is a *sufficient condition* for being male. If a person is not a father, nothing can be said about if they are male. Whereas if a person is not male, they may not be a father. This last statement is the *contrapositive* of the proposition.

p|q|-p|-q|p->q|-q->-p---+---+----+----+--------+---------- T | T | F | F | T | T T | F | F | T | F | F F | T | T | F | T | T F | F | T | T | T | T

where *–* represents negation. Since both *p* -> *q* and *-q* -> *-p* have identical truth tables they are said to be *logically equivalent*.

Thanks you so much for this table. I just couldn’t find any website that explained p implies q in simple English. Please add more examples.