Practice Biconditional in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A biconditional P \leftrightarrow Q is true when P and Q have the same truth value — both true or both false.
'P if and only if Q'—they're equivalent, true together or false together.
Example 1
easyEvaluate the biconditional p \Leftrightarrow q for all truth value combinations and construct its truth table.
Example 2
mediumDetermine whether 'n is even \Leftrightarrow n^2 is even' is true for all integers n.
Example 3
easyState whether each biconditional is true or false: (a) '3 = 3 \Leftrightarrow 5 > 2', (b) '3 = 4 \Leftrightarrow 1 = 2', (c) '3 = 3 \Leftrightarrow 1 = 2'.
Example 4
mediumVerify that p \Leftrightarrow q \equiv (p \Rightarrow q) \land (q \Rightarrow p) using a truth table.