P(A) > P(B) if and only if event A is more likely to occur then event B.

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

• if P(A) > P(B), then event A is more likely to occur then event B.
• if event A is more likely to occur then event B, then P(A) > P(B).
• if P(A) ≤ P(B), then event A is NOT more likely to occur then event B.
• if event A is NOT more likely to occur then event B, then P(A) ≤ P(B).

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: P(A) > P(B)

Q: event A is more likely to occur then event B

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

• (Conditional sentence: "If P then Q" [P → Q]) if P(A) > P(B), then event A is more likely to occur then event B.
• (Converse: "If Q then P" [P ← Q]) if event A is more likely to occur then event B, then P(A) > P(B).
• (Inverse: "If ~P then ~Q" [~P → ~Q]) if P(A) ≤ P(B), then event A is NOT more likely to occur then event B.
• (Contrapositive: "If ~Q then ~P" [~P ← ~Q]) if event A is NOT more likely to occur then event B, then P(A) ≤ P(B).