# If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find

(i) A ∩ B (ii) B ∩ C (iii) A ∩ C ∩ D (iv) A ∩ C (v) B ∩ D (vi) A ∩ (B ∪ C)

(vii) A ∩ D (viii) A ∩ (B ∪ D) (ix) ( A ∩ B ) ∩ ( B ∪ C ) (x) ( A ∪ D) ∩ ( B ∪ C)

**Solutions:**

The intersection of two sets A and B is a set that is obtained by writing all the elements that are common in both sets A and B.

Thus,

(i) A ∩ B = {7, 9, 11}

(ii) B ∩ C = {11, 13}

(iii) A ∩ C ∩ D = {A ∩ C} ∩ D = {11} ∩ {15, 17} = Φ

(iv) A ∩ C = {11}

(v) B ∩ D = Φ

(vi) A ∩ (B υ C) = (A ∩ B) υ (A ∩ C) = {7, 9, 11} υ {11} = {7, 9, 11}

(vii) A ∩ D = Φ

(viii) A ∩ (B υ D) = (A ∩ B) υ (A ∩ D) = {7, 9, 11} υ Φ = {7, 9, 11}

(ix) (A ∩ B) ∩ ( B υ C) = {7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11}

(x) (A υ D) ∩ (B υ C) = {3, 5, 7, 9, 11, 15, 17} ∩ {7, 9, 11, 13, 15} = {7, 9, 11, 15}

### NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.4 Question 6

## If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (i) A ∩ B (ii) B ∩ C (iii) A ∩ C ∩ D (iv) A ∩ C (v) B ∩ D (vi) A ∩ (B ∪ C) (vii) A ∩ D (viii) A ∩ (B ∪ D) (ix) ( A ∩ B ) ∩ ( B ∪ C ) (x) ( A ∪ D) ∩ ( B ∪ C)

**Summary:**

If A = { 3, 5, 7, 9, 11 }, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}, then we found that

(i) A ∩ B = {7, 9, 11}

(ii) B ∩ C = {11, 13}

(iii) A ∩ C ∩ D = {A ∩ C} ∩ D = {11} ∩ {15, 17} = Φ

(iv) A ∩ C = {11}

(v) B ∩ D = Φ

(vi) A ∩ (B υ C) = (A ∩ B) υ (A ∩ C) = {7, 9, 11} υ {11} = {7, 9, 11}

(vii) A ∩ D = Φ

(viii) A ∩ (B υ D) = (A ∩ B) υ (A ∩ D) = {7, 9, 11} υ Φ = {7, 9, 11}

(ix) (A ∩ B) ∩ ( B υ C) = {7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11}

(x) (A υ D) ∩ (B υ C) = {3, 5, 7, 9, 11, 15, 17} ∩ {7, 9, 11, 13, 15} = {7, 9, 11, 15}

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