Operations on sets+ cartesian product

Chapter 2 Class 11 Relations and Functions
Concept wise

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

### 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.