Boolean expressions with variables: truth tables

We can obtain the value of a boolean expression with variables by substituting each variable with its truth value, and simplifying according to the meaning of the operators. To characterize the meaning of a boolean expression, we can construct a table in which, for each possible combination of truth values for the variables, we specify the truth value of the whole expression. Such a table is called a truth table.

Truth tables for the boolean operators

a	b	a and b
true	true	true
false	true	false
true	false	false
false	false	false

a	b	a or b
true	true	true
false	true	true
true	false	true
false	false	false

a	not a
true	false
false	true

Example:     

a	b	c	(a and (not b)) or c
true	true	true	true
false	true	true	true
true	false	true	true
false	false	true	true
true	true	false	false
false	true	false	false
true	false	false	true
false	false	false	false