# Disjunction

How to find the truth value of the disjunction of two statements: definition, truth value, 2 examples, and their solutions.

## Definition

## Thuth Value

[p ∨ q] means [p or q].

So if either p or q is true,

p ∨ q is true.

If both p and q are all false,

p ∨ q is false.

## Example

Solution

Solution (Detail)

p: 5 is a positive number.

This is true.

p is true.

Then p ∨ q is true.

It doesn't matter

whether q is true or not.

[p is true] makes [p or q] true.

So true is the answer.

## Example

Solution

Solution (Detail)

q: 1 + 1 = 3

This is false.

s: 2 > 9

This is also false.

Both q and s are all false.

So q ∨ s is false.

So false is the answer.