Conjunction Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

Let

p

: '

4

is even' and

q

: '

4 < 10

'. Evaluate

p \land q

p \land \neg q

, and

\neg p \land q

1
$p$ is true (4 is even). $q$ is true (4 < 10). So $\neg q$ is false and $\neg p$ is false.
2
$p \land q = T \land T = T$ .
3
$p \land \neg q = T \land F = F$ .
4
$\neg p \land q = F \land T = F$ .

Answer

p \land q = T,\quad p \land \neg q = F,\quad \neg p \land q = F

A conjunction

p \land q

is true only when both components are true. If either component is false, the conjunction is false.

About Conjunction

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.

Construct the full truth table for [formula] and use it to show that conjunction is commutative: [fo

Determine the truth value of: (a) '[formula] and [formula]', (b) '[formula] and [formula]'.

Simplify: find all [formula] satisfying '[formula] and [formula]', and express as an interval.