# Disjunction

How to solve the disjunction of two statements problems: its truth values, examples, and their solutions.

## Truth Value

*p* ∨ *q* is the disjunction of *p* and *q*.

It means '*p* or *q*'.

So *p* ∨ *q* is true

if either *p* or *q* is true.

This is the difference between

the truth value of a conjunction: *p* ∧ *q*.

## Example 1

'*p*: 5 is a positive number' is true.

So '*p* ∨ *q*' is true.

You don't need to find the truth value of *q*,

because '*p* is true' is enough to make *p* ∨ *q* true.

## Example 2

'*q*: 1 + 1 = 3' is false.

'*r*: 2 > 9' is false.

So '*q* ∧ *r*' is false.