Boolean Algebra Calculator

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Enter a boolean expression such as A ^ (B v C) in the box and click Parse.

Supported operations are AND, OR, NOT, XOR, IMPLIES, PROVIDED and EQUIV.

Operations and constants are case-insensitive.

Variables are case sensitive, can be longer than a single character, can only contain alphanumeric characters, digits and the underscore character, and cannot begin with a digit.

Operations

Operations are executed in order of precedence, from higher to lower. Operations with the same precedence are executed from left to right. To execute a particular operation first, surround it with parenthesis ( ).

Operation	Aliases	Evaluates to `true` if	Evaluates to `false` if	Precedence
`NOT A`	`~ ' ! ¬`	`A` is `false`.	`A` is `true`.	highest
`A AND B`	`∧ ^ & · *`	both `A` and `B` are `true`.	either or both are `false`.	middle
`A EQUIV B`	`⇔ ≡ ↔ =`	both `A` and `B` are `true`; or both are `false`.	one is `true` and the other is `false`.	middle
`A IMPLIES B`	`⇒ → ⊂ <`	`A` is `false`; or `A` is `true` and `B` is `true`.	`A` is `true` and `B` is `false`.	middle
`A PROVIDED B`	`⇐ ← ⊃ >`	`A` is `true` and `B` is `true`; or `B` is `false`.	`A` is `false` and `B` is `true`.	middle
`A OR B`	`∨ v + ∥ \|`	`A` is `true`; `B` is `true`; or both are `true`.	both are `false`.	lowest
`A XOR B`	`⊻ ⊕`	`A` is `true` and `B` is `false`; or `A` is `false` and `B` is `true`.	both are `true` or both are `false`.	lowest

Constants

Constant	Aliases	Description
`TRUE`	`1 T ⊤ true`	Always evaluates to `true`.
`FALSE`	`0 F ⊥ false`	Always evaluates to `false`.