Operations on sets+ cartesian product
Operations on sets+ cartesian product
Last updated at April 16, 2024 by Teachoo
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