# Conjunction

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

## Definition

## Thuth Value

[p ∧ q] means [p and q].

So if both p and q are all true,

p ∧ q is true.

Otherwise,

p ∧ q is false.

## Example

Solution

Solution (Detail)

p: 5 is a positive number.

This is true.

q: 1 + 1 = 3

This is false.

p is true.

q is false.

So p ∧ q is false.

So false is the answer.

## Example

Solution

Solution (Detail)

p: 5 is a positive number.

This is true.

r: 4 > 2

This is true.

Both p and r are all true.

So p ∧ r is true.

So true is the answer.