Intersection of Sets
Last updated at April 16, 2024 by Teachoo
Ex 1.4, 7 If A = {x: x is a natural number}, B ={x: x is an even natural number}, C = {x: x is an odd natural number} and D = {x: x is a prime number}, Find First, let’s write all the sets in roster form A = {x: x is a natural number} = {1, 2, 3, 4, 5 …} B = {x: x is an even natural number} = {2, 4, 6, 8 …} C = {x: x is an odd natural number} = {1, 3, 5, 7, 9 …} D = {x: x is a prime number} = {2, 3, 5, 7 …} Ex 1.4, 7 (i) A ∩ B A = {1, 2, 3, 4, 5 …} B = {2, 4, 6, 8 …} C = {1, 3, 5, 7, 9 …} D = {2, 3, 5, 7 , 11,13 …} A ∩ B = {1, 2, 3, 4, 5 …} ∩ {2, 4, 6, 8 …} = {2, 4, 6, 8, ..} = B Ex 1.4, 7 (ii) A ∩ C A = {1, 2, 3, 4, 5 …} B = {2, 4, 6, 8 …} C = {1, 3, 5, 7, 9 …} D = {2, 3, 5, 7 , 11,13 …} A ∩ C = {1, 2, 3, 4, 5 …} ∩ {1, 3, 5, 7, 9 …} = {1, 3, 5, 7, 9,…} = C Ex 1.4, 7 (iii) A ∩ D A = {1, 2, 3, 4, 5 …} B = {2, 4, 6, 8 …} C = {1, 3, 5, 7, 9 …} D = {2, 3, 5, 7 , 11,13 …} A ∩ D = {1, 2, 3, 4, 5 …} ∩ {2, 3, 5, 7 …} = {2, 3, 5, 7,…} = D Ex 1.4, 7 (iv) B ∩ C A = {1, 2, 3, 4, 5 …} B = {2, 4, 6, 8 …} C = {1, 3, 5, 7, 9 …} D = {2, 3, 5, 7 , 11,13 …} B ∩ C = {2, 4, 6, 8 …} ∩ {1, 3, 5, 7, 9 …} = { } = ∅ Ex 1.4, 7 (v) B ∩ D A = {1, 2, 3, 4, 5 …} B = {2, 4, 6, 8 …} C = {1, 3, 5, 7, 9 …} D = {2, 3, 5, 7 , 11,13 …} B ∩ D = {2, 4, 6, 8 …} ∩ {2, 3, 5, 7, …} = {2} Ex 1.4, 7 (vi) C ∩ D A = {1, 2, 3, 4, 5 …} B = {2, 4, 6, 8 …} C = {1, 3, 5, 7, 9 …} D = {2, 3, 5, 7 , 11,13 …} C ∩ D = {1, 3, 5, 7, 9 …} ∩ {2, 3, 5, 7 …} = {3, 5, 7, 11, 13, 17, 19…} = {x: x is odd prime number} Prime number = 2, 3, 5, 7, 11, 13,…. Odd prime number = 3, 5, 7, 11, 13,….