In Boolean algebra, the order of operations is important. Parentheses can be used to group expressions and ensure that they are evaluated in the correct order.

The dual of a Boolean expression is obtained by interchanging ∧ and ∨, and 0 and 1.

A tautology is a Boolean expression that is always true, regardless of the values of its variables.

The distributive law states that the operation of ∨ over ∧ is distributive.

The associative law states that the operation of ∨ is associative.

The identity element for the operation of ∧ is the element that, when combined with any other element, leaves that element unchanged.

The identity element for the operation of ∨ is the element that, when combined with any other element, leaves that element unchanged.

The complement of a Boolean expression is the expression that is true when the original expression is false, and vice versa.

The complement of a Boolean expression is the expression that is true when the original expression is false, and vice versa.

De Morgan's law states that the negation of a conjunction is the disjunction of the negations, and vice versa.

The contrapositive of a statement is the statement that is formed by negating both the hypothesis and the conclusion.

The converse of a statement is the statement that is formed by interchanging the hypothesis and the conclusion.

The inverse of a statement is the statement that is formed by negating the hypothesis.

The negation of a universal statement is an existential statement that denies the universal claim.

The negation of an existential statement is a universal statement that denies the existential claim.