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 [math]\wedge[/math], returns the value "true" if and only if both arguments are true.

[math]\wedge[/math] : This is the conjunction or AND operator

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


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

Truth table for conjunction statements

[math]p \,\![/math] [math]q \,\![/math] [math]p \wedge q[/math]
T T T
T F F
F T F
F F F

Next lesson

Your next lesson is called Logical OR.