A Biconditional Sentence

A natural number is divisible by 3 if and only if the sum of the digits of the natural number is divisible by 3.


The biconditional sentence above compactly states the following four conditional sentences:


More on Biconditional Sentences

If "P" represents one statement and "Q" represents another statement, then "If P then Q" is called a conditional sentence symbolized as "P → Q"


The following four conditional sentences can be considered:

Biconditional Sentence Consequences

The biconditional sentence P if and only if Q states that the conditional sentence, its converse, inverse and contrapositive are all true.


The biconditional sentence of this example can be broken up into the two parts below.


P: natural number is divisibly by 3

Q: the sum of the digits of the natural number is divisible by 3


P if and only if Q [i.e. P Q] results in the following: