Practice Conjunction in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A conjunction P \wedge Q is a compound statement that is true if and only if both constituent statements P and Q are individually true.
To enter a theme park ride, you must be tall enough AND have a valid ticket—both conditions must hold. If you are tall enough but lost your ticket, you cannot ride. A conjunction P \wedge Q works the same way: it is true only when every single part is true, and false the moment any part fails.
Example 1
easyLet p: '4 is even' and q: '4 < 10'. Evaluate p \land q, p \land \neg q, and \neg p \land q.
Example 2
mediumConstruct the full truth table for p \land q and use it to show that conjunction is commutative: p \land q \equiv q \land p.
Example 3
easyDetermine the truth value of: (a) '3 > 2 and 3 < 5', (b) '3 > 2 and 3 > 5'.
Example 4
mediumSimplify: find all x \in \mathbb{R} satisfying 'x > 1 and x < 4', and express as an interval.