Question

Find whether the following statement is "True or False". Justify your answer
(A-B) U (AnB) = A

Answer 1

Answer

Refer to the attachment

Answer 2

(A-B) U (AnB) = A is true

Given:

(A-B) U (AnB) = A

To Find:

Whether the subsequent statement is "True or False" from the question given as (A-B) U (AnB) = A

Solution:

A union B complement could be a formula in pure mathematics that's capable of the intersection of the enhancement of the sets A and B.

A union B union C complement consists of parts of the universal set that aren't in any of the sets A, B, and C.

To prove that,

A = (A-B) U (B)

We have,

Say x∈A

Case(1):

Say x∈B

x ∈ A∩B

Then we've,

x ∈ ( A∩B) ∪ (A -B)

Case (2):

Say x ∉ B

= x ∈ A-B

= x ∈ ( A∩B) ∪ (A -B)

⇒ ( A∩B) ∪ (A -B) ⊂A

From (1) and (2),

A = ( A∩B) ∪ (A -B)

Hence, we tend to get that (A-B) U (AnB) = A is often true

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