Question

If A= {2, 3, 4, 5, 7}, B= {1,2, 4, 7, 9} then ( ( A-B ) U (B-A)) ∩ A is equal to

Answer 1

Answer:

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Symmetric Difference using Venn Diagram

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The symmetric difference using Venn diagram of two subsets A and B is a sub set of U, denoted by A △ B and is defined by

A △ B = (A – B) ∪ (B – A)

Let A and B are two sets. The symmetric difference of two sets A and B is the set (A – B) ∪ (B – A) and is denoted by A △ B.

Thus, A △ B = (A – B) ∪ (B – A) = {x : x ∉ A ∩ B}

or, A △ B = {x : [x ∈ A and x ∉ B] or [x ∈ B and x ∉ A]}

Symmetric Difference using Venn Diagram

The shaded part of the given Venn diagram represents A △ B.

Answer 2

Answer:

The value of ((A-B) U (B-A))∩A = {3,5}

Step-by-step explanation:

Given sets A = {2, 3, 4, 5, 7} and B = {1, 2, 4, 7, 9}

 We need to find ((A-B) U (B-A))∩A

  Since, A-B = {x: x∈ A and x∉ B}

   Now, A-B = { 3, 5}          ----------------(i)

  Since, B-A = {x: x∈ B and x∉ A}

   Now, B-A = {1, 9}         -----------------(ii)

  Take Unioun of (i) and (ii)

    AUB = { x: x∈ A or x ∈ B}

So,   (A-B) U (B-A) = {x: x∈ (A-B) or x ∈ (A-B)}

                             = {1,3,5,9}

Since A∩B = { x: x∈ A and x ∈ B}

Now, ((A-B) U (B-A))∩A = { x: x∈ (A-B) U (B-A) and x ∈ A}

                                      = {3,5}

Hence, ((A-B) U (B-A))∩A = {3, 5}

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