Question

what is the value of {(A U A)'}'​

Answer 1

Answer:

U(union) is correct answer

Answer 2

Answer:

The value of {(A ∪ A)'}' is A.

Step-by-step explanation:

Union of sets:-

• For any two sets A and B, the union of A and B is the set which consists of all the elements of A and all the elements of B.
• The common elements of the sets A and B is considered only once.

Compliment of a set:-

• Let A is a subset of U (Universal set). Then the compliment of A is defined as the set of those elements of U which are not the elements of A.
• Mathematically, A' = U - A
• A' is the compliment of A
• (A')' = A

Step 1 of 1

Consider the given condition as follows:

{(A ∪ A)'}'

Since A ∪ A = A

⇒ {(A ∪ A)'}' = {(A)'}' . . . . . (1)

Now,

The compliment of the set A is,

A' = U - A

Again,

The compliment of the set A' is,

(A')' = (U - A)'

      = U - (U - A)

      = A

Substitute the value of (A')' in the (1), we get

{(A ∪ A)'}' = A

Therefore, the value of {(A ∪ A)'}' is A.

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