**How to Find Complement of Union and Intersection of a Set ?**

Here we are going to see some practice problems of finding complement of union and intersection of a set.

**Question 1 :**

If U = {a, b, c, d, e, f, g, h}, A = {b, d, f, h} and B = {a, d, e, h}, find the following sets.

(i) A′ (ii) B′ (iii) A′∪B′ (iv) A′∩B′ (v) (A∪B)′

(vi) (A∩B)′ (vii) (A′)′ (viii) (B′)′

**Solution :**

(i) A' = {a, c, e, g}

(ii) B' = {b, c, f, g}

(iii) A′∪B′ = { a, b, c, e, g }

(iv) A′∩B′ = { c, g }

(v) (A∪B)′

To find (A∪B)′, first we have to find A U B

A U B = {a, b, d, e, f, h}

(A U B)' = {c, g}

(vi) (A∩B)′ = {a, b, c, e, g }

(vii) (A′)′

A = {b, d, f, h}

(viii) (B′)′

B = {a, d, e, h}

**Question 2 :**

Let U = {0, 1, 2, 3, 4, 5, 6, 7}, A = {1, 3, 5, 7} and B = {0, 2, 3, 5, 7}, find the following sets.

(i) A′ (ii) B′ (iii) A′∪B′ (iv)A′∩B′ ( v)(A∪B)′

(vi) (A∩B)′ (vii) (A′)′ (viii) (B′)′

**Solution :**

(i) A' = {0, 2, 4, 6}

(ii) B' = {1, 4, 6}

(iii) A′∪B′ = {0, 1, 2, 4, 6 }

(iv) A′∩B′ = {4, 6}

(v) (A∪B)′

To find (A∪B)′, first we have to find A U B

A U B = {0, 1, 2, 3, 5, 7}

(A U B)' = {4, 6}

(vi) (A∩B)′ = {0, 1, 2, 4, 6 }

(vii) (A′)′

{1, 3, 5, 7}

(viii) (B′)′

B = {0, 2, 3, 5, 7}

**Question 3 :**

Find the symmetric difference between the following sets.

(i) P = {2, 3, 5, 7, 11} and Q = {1, 3, 5, 11}

**Solution :**

P Δ Q = (P - Q) U (Q - P)

P - Q = {2, 7}

Q - P = {1, 11}

(P - Q) U (Q - P) = {1, 2, 7, 11}

Hence the value of P Δ Q is {1, 2, 7, 11}

(ii) R = {l, m, n, o, p} and S = {j, l, n, q}

**Solution :**

R Δ S = (R - S) U (S - R)

R - S = {m, o , p}

S - R = {j, q}

(R - S) U (S - R) = {j, m, o, p, q}

Hence the value of R Δ S is {j, m, o, p, q}.

(iii) X = {5, 6, 7} and Y = {5, 7, 9, 10}

**Solution : **

X Δ Y = (X - Y) U (Y - X)

X - Y = {6}

Y - X = {9, 10}

(X - Y) U (Y - X) = {6, 9, 10}

Hence the value of X Δ Y is {6, 9, 10}.

After having gone through the stuff given above, we hope that the students would have understood, "How to Find Complement of Union and Intersection of a Set".

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