Question

For all sets A and B, A-(A intersection B) is equal to

Answer 1

A-(A intersection B)=A-B

Answer 2

Answer:

For A ⊆ B, A - (A ∩ B) = ∅ and,

For B ⊆ A, A - (A ∩ B) = A - B.

Step-by-step explanation:

Intersection: Set of elements which belong to A and B both. Mathematically, A ∩ B = {x : x ∈ A and x ∈ B}

Difference of sets: The sets of elements which belong to A but not to B is called the difference of sets. Symbolically, A-B.

Given: A and B are sets.

To find: A - (A ∩ B)

Case1. When A is a subset of B, i.e., A ⊆ B.

⇒ A ∩ B = A

Then,

$A$ - (A ∩ B) = $A-A$

                 = ∅

Here, ∅ is used to denote the empty set.

Thus, A - (A ∩ B) = ∅.

Case2. When B is a subset of A, i.e., B ⊆ A.

⇒ A ∩ B = B

Then,

A - (A ∩ B) = A - B.

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