Check sibling questions

Ex 2.1, 7 - Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6}

Ex 2.1, 7 - Chapter 2 Class 11 Relations and Functions - Part 2
Ex 2.1, 7 - Chapter 2 Class 11 Relations and Functions - Part 3

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Ex 2.1, 7 Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that A × (B ∩ C) = (A × B) ∩ (A × C) ∩ Intersection : Common between two sets A × (B ∩ C) B ∩ C = {1, 2, 3, 4} ∩ {5, 6} = ϕ A × (B ∩ C) = {1, 2} × ϕ = ϕ (A × B) ∩ (A × C) A × B = {1, 2} × {1, 2, 3, 4} = {(1, 1), (1, 2) , (1, 3), (1, 4), (2, 1), (2, 2) , (2, 3), (2, 4)} A × C = {1, 2} × {5, 6} = { (1, 5), (1, 6), (2, 5), (2, 6)} (A × B) ∩ (A × C) = ϕ Since L.H.S = R.H.S Hence proved Ex 2.1, 7 Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that (ii) A × C is a subset of B × D A × C = {1, 2} × {5, 6} = {(1, 5), (1, 6), (2, 5), (2, 6)} Since All the elements of set A × C are the elements of set B × D. ∴ A × C is a subset of B × D. ⊂ - is a subset A ⊂ B if all elements of A are in B B × D = {1, 2, 3, 4} × {5, 6, 7, 8} = {(1, 5), (1, 6), (1, 7), (1, 8), (2, 5), (2, 6), (2, 7), (2, 8), (3, 5), (3, 6), (3, 7), (3, 8), (4, 5), (4, 6), (4, 7), (4, 8)}

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.