Disjunction Math Example 2

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

medium

Find all real

x

satisfying '

x < -1

x > 3

', and express as a union of intervals.

1
The disjunction holds when at least one of the two inequalities is satisfied.
2
Solution set of $x < -1$ : $(-\infty, -1)$ . Solution set of $x > 3$ : $(3, \infty)$ .
3
The union is $(-\infty,-1) \cup (3,\infty)$ .

Answer

x \in (-\infty,-1) \cup (3,\infty)

A disjunction corresponds to the union of the individual solution sets. The region between

-1

and

3

is excluded because neither condition holds there.

About Disjunction

A disjunction $P \vee Q$ is a compound statement that is true whenever at least one of its parts is true.

Let [formula]: '[formula] is even' and [formula]: '[formula] is odd'. Evaluate [formula] and explain

Evaluate: (a) 'F [formula] T', (b) 'F [formula] F', (c) 'T [formula] T'.

Use a truth table to verify De Morgan's Law: [formula].