Ex 1.4, 7

Transcript

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 (i) A ∩ B 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 …} A ∩ B = {1, 2, 3, 4, 5 …} ∩ {2, 4, 6, 8 …} = {2,4,6,8,..} = 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 …} Ex 1.4,7 (ii) A ∩ C A ∩ C = {1, 2, 3, 4, 5 …} ∩ {1, 3, 5, 7, 9 …} = {1,3,5,7,9,…} = 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 …} Ex 1.4,7 (iii) A ∩ D A ∩ D = {1, 2, 3, 4, 5 …} ∩ {2, 3, 5, 7 …} = {2,3,5,7,…} = 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 …} Ex 1.4,7 (iv) B ∩ C B ∩ C = {2, 4, 6, 8 …} ∩ {1, 3, 5, 7, 9 …} = { } = ∅ A = {1, 2, 3, 4, 5 …} B = {2, 4, 6, 8 …} C = {1, 3, 5, 7, 9 …} D = {2, 3, 5, 7 , 11,13 …} Ex 1.4,7 (v) B ∩ D B ∩ D = {2, 4, 6, 8 …} ∩ {2, 3, 5, 7, …} = {2} A = {1, 2, 3, 4, 5 …} B = {2, 4, 6, 8 …} C = {1, 3, 5, 7, 9 …} D = {2, 3, 5, 7, 11,13 …} Ex 1.4,7 (vi) C ∩ D C ∩ D = {1, 3, 5, 7, 9 …} ∩ {2, 3, 5, 7 …} = {3,5,7,11,13,17,19…} = {x: x is odd prime number}