Last updated at Jan. 27, 2020 by Teachoo

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Ex 1.5, 1 Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (i) A’ A’ = U – A = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {1, 2, 3, 4} = {5, 6, 7, 8, 9} Ex 1.5, 1 Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (ii) B’ B’ = U – B = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 4, 6, 8} = {1, 3, 5, 7, 9} Ex 1.5, 1 (Method 1) Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (A ∪ C)’ A ∪ C = {1, 2, 3, 4} ∪ {3, 4, 5, 6} = {1, 2, 3, 4 ,5 ,6} (A ∪ C)’ = U – (A ∪ C) = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {1, 2, 3, 4, 5, 6} = {7, 8, 9} ∪ Union - Combination of two sets Ex 1.5, 1 (Method 2) Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (A ∪ C)’ (A ∪ C)’ = A’ ∩ C’ A’ = U – A = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {1, 2, 3, 4} = { 5, 6, 7, 8, 9} ∪ Union - Combination of two sets ∩ Intersection – Common of two sets C’ = U – C = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {3, 4, 5, 6} = { 1, 2, 7, 8, 9} (A ∪ C)’ = A’ ∩ C’ = {5, 6, 7, 8, 9} ∩ {1, 2, 7, 8, 9} = {7, 8, 9} Ex 1.5, 1 (Method 1) Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (A ∪ B)’ A ∪ B = {1, 2, 3, 4} ∪ {2, 4, 6, 8} = {1, 2, 3, 4, 6, 8} (A ∪ B)’ = U – (A ∪ B) = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {1,2,3,4,6,8} = {5, 7, 9} ∪ Union - Combination of two sets Ex 1.5, 1 (Method 2) Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (iv) (A ∪ B)’ (A ∪ B)’ = A’ ∩ B’ A’ = U – A = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {1, 2, 3, 4} = { 5, 6, 7, 8, 9} ∪ Union - Combination of two sets ∩ Intersection – Common of two sets B’ = U – B = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2, 4, 6, 8} = { 1, 3, 5, 7, 9} (A ∪ B)’ = A’ ∩ B’ = { 5, 6, 7, 8, 9} ∩ { 1, 3, 5, 7, 9} = {5, 7, 9} Ex 1.5, 1 (Method 1) Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (v) (A’)’ (A’)’ = A = {1, 2, 3, 4} Ex 1.5, 1 (Method 2) Let U ={1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (v) (A’)’ (A’)’ = U – A’ A’ = U – A = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {1, 2, 3, 4} = {5, 6, 7, 8, 9} (A’)’ = U – A’ = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {5, 6, 7, 8, 9} = {1, 2, 3, 4} = A Ex 1.5, 1 Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find (vi) (B – C)’ B – C = B – (B ∩ C) B ∩ C = {2, 4, 6, 8} ∩ {3, 4, 5, 6} = {4, 6} B – C = B – (B ∩ C) = {2, 4, 6, 8} – {4, 6} = { 2,8 } A – B = A – (A ∩ B) ∩ Intersection – Common of two sets (B – C)’ = U – (B – C) = {1, 2, 3, 4, 5, 6, 7, 8, 9} – {2 , 8} = {1, 3, 4, 5, 6, 7, 9}

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.