Intersection of Sets

Chapter 1 Class 11 Sets
Concept wise

### Transcript

Ex 1.4, 6 If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find A ∩ B A ∩ B = {3, 5, 7, 9, 11} ∩ {7, 9, 11, 13} = {7, 9, 11} ∩ Intersection – Common of two sets Ex 1.4, 6 If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (ii) B ∩ C B ∩ C = {7, 9, 11, 13} ∩ {11, 13, 15} = {11, 13} Ex 1.4, 6 If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (iii) A ∩ C ∩ D A ∩ C ∩ D = (A ∩ C) ∩ D (A ∩ C) = {3, 5, 7, 9, 11} ∩ {11, 13 ,15} = {11} ∩ Intersection – Common of two sets A ∩ C ∩ D = (A ∩ C) ∩ D = {11} ∩ {15, 17} = { } = ∅ Ex 1.4, 6 If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (iv) A ∩ C A ∩ C = {3, 5, 7, 9, 11} ∩ {11, 13, 15} = {11} ∩ Intersection – Common of two sets Ex 1.4, 6 If A = {3, 5, 7, 9, 11} B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (v) B ∩ D B ∩ D = {7, 9, 11, 13} ∩ {15, 17} = { } = ∅ ∩ Intersection – Common of two sets Ex 1.4, 6 (Method 1) If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (vi) A ∩ (B ∪ C) B ∪ C = {7, 9 , 11, 13} ∪ {11, 13 ,15} = { 7, 9, 11, 13, 15} A ∩ (B ∪ C) = {3, 5, 7, 9, 11} ∩ { 7,9,11,13,15} = {7, 9, 11} ∪ Union - Combination of two sets ∩ Intersection – Common of two sets Ex 1.4, 6 (Method 2) If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (vi) A ∩ (B ∪ C) A ∩ (B ∪ C) = (A ∩ B) = {3, 5, 7, 9, 11} ∩ {7, 9 , 11, 13} = {7, 9, 11} (A ∩ C) = {3, 5, 7, 9, 11} ∩ {11, 13 ,15} = {11} ∪ Union - Combination of two sets ∩ Intersection – Common of two sets As 2 × (3 + 4) = 2 × 3 + 2 × 4 Now, A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C) = {7, 9, 11} ∪ {11} = {7, 9, 11} Ex 1.4, 6 If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (vii) A ∩ D A ∩ D = {3, 5, 7, 9, 11} ∩ {15, 17} = { } = ∅ ∩ Intersection – Common of two sets Ex 1.4, 6 (Method 1) If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (viii) A ∩ (B ∪ D) B ∪ D = {7, 9 , 11, 13} ∪ {15 ,17} = {7, 9, 11, 13, 15, 17} A ∩ (B ∪ D) = {3, 5, 7, 9, 11} ∩ { 7, 9, 11, 13, 15, 17} = {7, 9, 11} ∪ Union - Combination of two sets ∩ Intersection – Common of two sets Ex 1.4, 6 (Method 2) If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (viii) A ∩ (B ∪ D) A ∩ (B ∪ D) = (A ∩ B) ∪ (A ∩ D) A ∩ B = {3, 5, 7, 9, 11} ∩ {7, 9 , 11, 13} = {7, 9, 11} ∪ Union - Combination of two sets ∩ Intersection – Common of two sets As 2 × (3 + 4) = 2 × 3 + 2 × 4 A ∩ D = {3, 5, 7, 9, 11} ∩ {15 ,17} = { } = ∅ A ∩ (B ∪ D) = (A ∩ B) ∪ (A ∩ D) = {7, 9, 11} ∪ ∅ = {7, 9, 11} Ex 1.4, 6 If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (ix) (A ∩ B) ∩ (B ∪ C) (A ∩ B) = {3, 5, 7, 9, 11} ∩ {7, 9 , 11, 13} = {7, 9, 11} (B ∪ C) = {7, 9 , 11, 13} ∪ {11, 13 ,15} = {7, 9, 11, 13, 15} (A ∩ B) ∩ (B ∪ C) = {7, 9, 11} ∩ {7, 9, 11, 13, 15} = {7, 9, 11} ∪ Union - Combination of two sets ∩ Intersection – Common of two sets Ex 1.4, 6 If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find (x) (A ∪ D) ∩ (B ∪ C) (A ∪ D) = {3, 5, 7, 9, 11} ∪ {15, 17} = {3, 5, 7, 9, 11, 15, 17} (B ∪ C) = {7, 9 , 11, 13} ∪ {11, 13 ,15} = {7, 9, 11, 13, 15} (A ∪ D) ∩ (B ∪ C) = {3, 5, 7, 9, 11, 15, 17} ∩ {7, 9, 11, 13, 15} = {7, 9, 11, 15} ∪ Union - Combination of two sets ∩ Intersection – Common of two sets