Biconditional

Definition

A biconditional is a logical statement that connects two propositions with 'if and only if,' indicating that both propositions are either simultaneously true or simultaneously false. It is often denoted by the symbol ↔ or the phrase 'iff'.

5 Must Know Facts For Your Next Test

1. The truth value of a biconditional statement (P ↔ Q) is true when both P and Q have the same truth value.
2. If P is true and Q is false, the biconditional statement P ↔ Q is false.
3. The biconditional statement can be broken down into two conditional statements: P → Q and Q → P.
4. In a truth table, a biconditional has four possible scenarios: TT, TF, FT, FF; it is true for TT and FF only.
5. A biconditional statement asserts equivalence between two propositions.

Review Questions

• What are the conditions under which a biconditional statement is true?
• How can you express a biconditional statement using conditional statements?
• What symbol or phrase denotes a biconditional statement?

Related terms

Conditional: A logical statement in the form 'if P then Q', where P implies Q.

Conjunction: A compound statement formed using the word 'and' to combine two statements, both of which must be true for the conjunction to be true.

Disjunction:

A compound statement formed using the word 'or' to combine two statements, where at least one of them must be true for the disjunction to be true.