A natural number is divisible by 4 if and only if the last two digits of the natural number are divisible by 4.

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

• if a natural number is divisible by 4, then the last two digits of the natural number are divisible by 4.
• if the last two digits of a natural number are divisible by 4, then the natural number is divisible by 4.
• if a natural number is NOT divisible by 4, then the last two digits of the natural number are NOT divisible by 4.
• if the last two digits of a natural number are NOT divisible by 4, then the natural number is NOT divisible by 4.

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:

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: a natural number is divisible by 4

Q: the last two digits of the natural number are ivisible by 4

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

• (Conditional sentence: "If P then Q" [P → Q]) if a natural number is divisible by 4, then the last two digits of the natural number are divisible by 4.
• (Converse: "If Q then P" [P ← Q]) if the last two digits of a natural number are divisible by 4, then the natural number is divisible by 4.
• (Inverse: "If ~P then ~Q" [~P → ~Q]) if a natural number is NOT divisible by 4, then the last two digits of the natural number are NOT divisible by 4.
• (Contrapositive: "If ~Q then ~P" [~P ← ~Q]) if the last two digits of a natural number are NOT divisible by 4, then the natural number is NOT divisible by 4.