AND

Definition

AND is a logical operator that combines two propositions.

It is true only when both propositions are true.

Example:

P AND Q

This means:

P is true and Q is true

AND requires both parts.

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Simple Example

Let:

P = "It is raining"
Q = "The ground is wet"

Then:

P AND Q

means:

It is raining and the ground is wet.

This compound proposition is true only if both statements are true.

If either part is false, the whole AND statement is false.

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Truth Pattern

AND has this truth pattern:

P      Q      P AND Q
true   true   true
true   false  false
false  true   false
false  false  false

Only the first row is true.

Both inputs must be true.

AND is strict: one false part makes the whole statement false.

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AND As Constraint

AND can express multiple requirements.

Example:

number is greater than 0 AND number is even

For:

number = 4

both parts are true.

For:

number = 3

the first part is true, but the second part is false.

So the whole statement is false.

AND narrows what counts as satisfying a statement.

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AND In Reasoning

If an AND statement is true, then each part is true.

Example:

P AND Q is true

Then we can infer:

P is true
Q is true

This makes AND useful for breaking compound statements into parts.

A true AND statement gives both components.

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Final Summary

• AND combines two propositions.
• It is true only when both propositions are true.
• If either part is false, the whole statement is false.
• AND expresses multiple requirements.
• A true AND statement lets us infer each component.