Propositional Logic Worksheet Page 13
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21Biconditionals
The biconditional of statements P and Q, denoted P ↔ Q, is
read “P if and only if Q” (or “P is necessary and sufficient for Q”),
and is true if P and Q have the same truth values, and false otherwise.
Example: Write down the truth table of P ↔ Q.
Example: True or false? 2+2 = 5 if and only if 2 is prime.
Example: true or false? 2+2 = 5 if and only if 10 is prime.
Note:
If P ↔ Q is true, then P → Q and Q → P are true.
Conversely if both P → Q and Q → P are true, then P ↔ Q is
true. Prove this claim using a truth table.
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