ASSOCIATIVE PROPERTY OF SET WORKSHEET
Associative property of set worksheet :
Here we are going to see some practice questions on associative property of set.
For any two two sets, the following statements are true.
(i) Set union is associative
A U (B U C) = (A U B) U C
(i) Set intersection is associative
A n (B n C) = (A n B) n C
Let us look into some example problems based on above properties.
Associative property of set worksheet - Practice questions
(1) Given, A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6} and C = {5, 6, 7, 8}, show that
(i) A U (B U C) = (A U B) U C. (ii) Verify (i) using Venn diagram.
(2) Let A = {a,b,c,d}, B = {a,c,e} and C = {a,e}.
(i) Show that A n (B n C) = (A n B) n C. (ii) Verify (i) using Venn diagram
(3) For A = {x ; x is a prime factor of 42}, B = {x | 5 x ≤ 12, x ∊ N} and C = {1, 4, 5, 6}, verify A U (B U C) = (A U B) U C
Associative property of set worksheet - Solution
Question 1 :
Given, A = {1, 2, 3, 4, 5}, B = {3, 4, 5, 6} and C = {5, 6, 7, 8}, show that
(i) A U (B U C) = (A U B) U C. (ii) Verify (i) using Venn diagram.
Solution :
Now, B U C = {3, 4, 5, 6} U {5, 6, 7, 8} = {3, 4, 5, 6, 7, 8}
A U (B U C) = {1, 2, 3, 4, 5} U { 3, 4, 5, 6, 7, 8}
= {1, 2, 3, 4, 5, 6, 7, 8} ----- (1)
Now, (A U B) = {1, 2, 3, 4, 5} U {3, 4, 5, 6} = {1,2,3,4,5,6}
(A U B) U C = {1,2,3,4,5,6} U {5,6,7,8}
= {1, 2, 3, 4, 5, 6, 7, 8} ----- (2)
(1) = (2)
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Question 2 :
Let A = {a,b,c,d}, B = {a,c,e} and C = {a,e}.
(i) Show that A n (B n C) = (A n B) n C. (ii) Verify (i) using Venn diagram
Solution :
Now, B n C = {a,c,e} n {a, e} = {a, e}
A n (B n C) = {a, b, c ,d} U {a, e}
= { a } ----- (1)
(A n B) = {a,b,c,d} n {a,c,e}
= {a, c}
(A n B) n C = {a, c} n {a,e}
= {a} ----- (2)
(1) = (2)
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Question 3 :
For A = {x ; x is a prime factor of 42}, B = {x | 5 x ≤ 12, x ∊ N} and C = {1, 4, 5, 6}, verify A U (B U C) = (A U B) U C
Solution :
A = {2, 3, 7}, B = {5, 6, 7, 8, 9, 10, 11, 12} and C = {1, 4, 5, 6}
(B U C) = {5, 6, 7, 8, 9, 10, 11, 12} U {1, 4, 5, 6}
= {1, 2, 4, 6, 8, 9, 10, 11, 12}
A U (B U C) = {2, 3, 7} U {1, 2, 4, 6, 8, 9, 10, 11, 12}
= {1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12} ----(1)
(A U B) = {2, 3, 7} U {5, 6, 7, 8, 9, 10, 11, 12}
= {2, 3, 5, 6, 7, 8, 9, 10, 11, 12}
(A U B) U C = {2, 3, 5, 6, 7, 8, 9, 10, 11, 12} U {1, 4, 5, 6}
= {1, 2, 3, 4, 6, 7, 8, 9, 10, 11, 12} ----(2)
(1) = (2)
Related topics
- Venn diagram A U B
- Venn diagram A n B
- Venn diagram of A'
- Venn diagram of B'
- Venn diagram of (AUB)'
- Venn diagram of (AnB)'
- Venn diagram of A\B
- Venn diagram of B\A
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