Identity Elements | MCQs

Explanation

The number 1 is called the multiplicative identity because multiplying any real number a by 1 leaves it unchanged: a × 1 = 1 × a = a.

This property holds for all real numbers (∀ a ∈ R).

Explanation

In the power set P(X), the intersection operation is defined as:

A ∩ B = {x ∈ X | x ∈ A and x ∈ B}

The identity element with respect to intersection is the element that does not change the result when intersected with any other element. In this case, the identity element is the set X itself, because:

A ∩ X = A

for any subset A of X.