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
- The truth value of a biconditional statement (P ↔ Q) is true when both P and Q have the same truth value.
- If P is true and Q is false, the biconditional statement P ↔ Q is false.
- The biconditional statement can be broken down into two conditional statements: P → Q and Q → P.
- In a truth table, a biconditional has four possible scenarios: TT, TF, FT, FF; it is true for TT and FF only.
- 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?
"Biconditional" appears in:
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.
