Operations on sets+ cartesian product

Chapter 2 Class 11 Relations and Functions
Concept wise

### Transcript

Example 3 Let A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}. Find A × (B ∩ C) B ∩ C = {3, 4} ∩ {"4, 5, 6" } = {"4" } A × (B ∩ C) = {"1, 2, 3" } × {"4" } = {"(1, 4), (2, 4), (3, 4)" } ∩ Intersection : Common between two sets Example 3 Let A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}. Find (ii) (A × B) ∩ (A × C) (A × B) = {"1, 2, 3" } × {"3, 4" } = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)} (A × B) ∩ (A × C) = {(1, 4), (2, 4), (3, 4)} ∩ Intersection : Common between two sets (A × C) = {"1, 2, 3" } × {"4, 5, 6" } = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)} Example 3 Let A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}. Find (iii) A × (B ∪ C) B ∪ C = {"3, 4" } ∪ {"4, 5, 6" } = {"3, 4, 5, 6" } A × (B ∪ C) = {"1, 2, 3" } × {"3, 4, 5, 6" } = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)} ∪ Union: Combination of two sets Example 3 Let A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}. Find (iv) (A × B) ∪ (A × C) (A × B) = {"1, 2, 3," }, × {"3, 4," }, = {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)} (A × B) ∪ (A × C) = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6)} (A × C) = {"1, 2, 3," } × {"4, 5, 6" }, = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)} ∪ Union: Combination of two sets

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#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.