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Logical AND

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Previous lesson: Using truth tables

Your first diadic operator!

I apologize for the name of this lesson. The true name of this operator, which is a diadic operator, is a conjunction. It is a bit dangerous to refer to a conjunction as an AND operator, because English words are far more vague than logic.

  • A diadic operator takes 2 arguments, p and q. It returns a single truth value.
  • The conjunction, represented by the symbol \wedge, returns the value "true" if and only if both arguments are true.

\wedge : This is the conjunction or AND operator

  • Let p represent the statement: It is raining.
Let q represent the statement: I am hungry.
p \wedge q represents the conjunction of statements p and q: It is raining AND I am hungry.


  • Let p represent the false statement: It is raining.
Let q represent the true statement: I am hungry.
p \wedge q is false.

Truth table for conjunction statements

p \,\! q \,\! p \wedge q
T T T
T F F
F T F
F F F

Next lesson

Your next lesson is called Logical OR.

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