**Practice questions on set operations answers :**

Here we are going to see some practice questions and solution of set operations.

**Question 1 :**

From the given Venn diagram find

(i) A (ii) B (iii) A U B (iv) A n B

Also verify that n(A U B) = n(A) + n(B) - n(A n B)

**Solution :**

The variables inside the circle A are known as elements of the set A.

A = { a, b, d, e, g, h }

The variables inside the circle B are known as elements of the set B.

B = { b, c, e, f, i, j, h }

The variables inside the circles A and B are known as elements of the set AUB.

A U B = { a, b, c, d, e, f, g, h, i, j }

The variables in the common region of A and B are known as elements of A n B.

A n B = { b, e, h }

To verify the given statement, we have to find the cardinal number of each set.

n (A) = 6

n (B) = 7

n (A U B) = 10

n (A n B) = 3

n(A U B) = n(A) + n(B) - n(A n B)

10 = 6 + 7 - 3

10 = 13 - 3

10 = 10

Hence it is proved.

**Question 2 :**

If n(U) = 38, n(A) = 16, n (AnB) = 12, n(B') = 20 find n(AUB) .

**Solution :**

n (A U B) = n (A) + n (B) - n (A n B)

n (B) = n (U) - n (B')

n (B) = 38 - 20 ==> 18

n (A U B) = n (A) + n (B) - n (A n B)

n (A U B) = 16 + 18 - 12

= 34 - 12

= 22

Hence the value of n (A U B) is 22.

**Question 3 :**

From the given Venn diagram find

(i) A (ii) B (iii) A U B (iv) A n B

Also verify that n(A U B) = n(A) + n(B) - n(A n B)

**Solution :**

The numbers inside the circle A are known as elements of set A.

A = { 2, 3, 4, 5, 6, 7, 8, 9 }

n (A) = 8

The numbers inside the circle B are known as elements of set B.

B = { 3, 6, 9 }

n (B) = 3

The numbers inside the circles A and B are known as elements of the set AUB.

A U B = { 2, 3, 4, 5, 6, 7, 8, 9 }

n (A U B) = 8

The numbers in common region of A and B is known as elements of A n B.

A n B = {3, 6, 9}

n (A n B) = 3

n(A U B) = n(A) + n(B) - n(A n B)

8 = 8 + 3 - 3

8 = 8

Hence it is proved.

Let us see the answer for next problem on "Practice questions on set operations answers".

**Question 4 :**

From the venn diagram, write the elements of set A n B

**Solution :**

The variables in common region of A and B are known as elements of A n B.

A n B = { b, e, h }

**Let us see the answer for next problem on "Practice questions on set operations answers".**

**Question 5 :**

If n(A) = 12, n(B) = 17 and n(A U B) = 21, find n(A n B)

**Solution :**

By using the formula,

n(A U B) = n (A) + n (B) - n (A n B)

we may find the value of n (A n B)

21 = 12 + 17 - n (A n B)

21 = 29 - n (A n B)

n (A n B) = 29 - 21 ==> 8

Hence the value of n (A n B) is 8.

**Question 6 :**

From the venn diagram, write the elements of the following sets

(i) A' (ii) B' (iii) (A n B)' (iv) (A U B)'

**Solution :**

(i) A'

A' = { c, f, i ,j }

(ii) B'

B' = { a, d, g }

(iii) (A n B)'

(A n B)' = { a, d, g, c, f, i, j }

(iv) (A U B)'

(A U B)' = { } (or) null set

**Question 7 :**

If n(U) = 43, n (A) = 26 find n (A')

**Solution :**

By using the formula,

n (A) + n (A') = n (U)

we may find the value of n (A')

26 + n (A') = 43

Subtract 26 on both sides

26 - 26 + n (A') = 43 - 26

n (A') = 17

Let us see the answer for next problem on "Practice questions on set operations answers".

**Question 8 :**

If n (U) = 38, n (A) = 16, n (A n B) = 12, n (B') = 20, find n (A U B).

**Solution :**

By using the formula,

n (B) + n (B') = n (U)

we may find the value of n (B')

n (B) + 20 = 38

Subtract 20 on both sides

n (B) + 20 - 20 = 38 - 20

n (B) = 18

n (A U B) = n (A) + n (B) - n (A n B)

= 16 + 18 - 12

= 34 - 12

= 22

Let us see the answer for next problem on "Practice questions on set operations answers".

**Question 9 :**

If A = {- 2, - 1,0,3,4}, B = {- 1,3,5}, find (i) A - B (ii) B - A

**Solution :**

A = {- 2, - 1,0,3,4} and B = {- 1,3,5}

A - B = { -2, 0, 4}

B - A = { 5 }

Let us see the answer for next problem on "Practice questions on set operations answers".

**Question 10 :**

If A = {2, 3, 5, 7, 11} and B = {5, 7, 9, 11, 13} , find A Δ B.

**Solution :**

A = {2, 3, 5, 7, 11} and B = {5, 7, 9, 11, 13}

A - B = { 2, 3 }

B - A = { 9, 13 }

A Δ B = (A - B) U (B - A)

= { 2, 3, 9, 13 }

Let us see the answer for next problem on "Practice questions on set operations answers".

**Question 11 :**

Given that U = {3, 7, 9, 11, 15, 17, 18}, M = {3, 7, 9, 11} and N = {7, 11, 15, 17},

find (i) M - N (ii) N - M (iii) N' - M (iv) M' - N

(v) M n (M - N) (vi) N U (N - M) (vii) n(M - N)

**Solution :**

U = { 3, 7, 9, 11, 15, 17, 18 }

M = { 3, 7, 9, 11 }

N = { 7, 11, 15, 17 }

(i) M - N

The set M - N would contain the elements of the set M excluding the elements of M n N

M - N = { 3, 9 }

(ii) N - M

The set N - M would contain the elements of the set M excluding the elements of N n M

N - M = { 15, 17 }

(iii) N' - M

N' = { 3, 9, 18 }

N' - M = {18}

(iv) M' - N

M' = { 15, 17, 18 }

M' - N = { 18 }

(v) M n (M - N)

The set M n (M - N) would contain the set of common elements that we found in both the set M and (M - N)

M = { 3, 7, 9, 11 } M - N = { 3, 9 }

M n (M - N) = { 3, 9}

(vi) N U (N - M)

N = { 7, 11, 15, 17 } N - M = { 15, 17 }

N U (N - M) = { 7, 11, 15, 17 }

(vii) n(M - N)

Number of elements of set M - N is 2.

Hence n(M - N) = 2

- Venn diagram A U B
- Venn diagram A n B
- Venn diagram of A'
- Venn diagram of B'
- Venn diagram of (AUB)'
- Venn diagram of (AnB)'
- Venn diagram of A\B
- Venn diagram of B\A

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