Disjunction Math Example 1

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

Example 1

easy
Let pp: '22 is even' and qq: '22 is odd'. Evaluate p∨qp \lor q and explain the result.

Solution

  1. 1
    pp: '22 is even' — True. qq: '22 is odd' — False.
  2. 2
    p∨q=T∨F=Tp \lor q = T \lor F = T.
  3. 3
    In logic, p∨qp \lor q (inclusive or) is true when at least one of pp, qq is true.

Answer

p∨q=Truep \lor q = \text{True}
The logical OR is inclusive: it is true whenever at least one operand is true, and false only when both are false. This differs from the everyday exclusive 'or' which excludes the case where both are true.

About Disjunction

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

Learn more about Disjunction →

More Disjunction Examples

Example 2 medium

Find all real [formula] satisfying '[formula] or [formula]', and express as a union of intervals.

Example 3 easy

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

Example 4 medium

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

← All Disjunction Examples Disjunction Concept