Sets
ICSE · Class 8 · Mathematics
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Quick Quiz: Sets
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A set X has 3 elements and set Y has 4 elements. If X and Y are disjoint, what is n(X ∪ Y)?
If n(A) = 8, n(B) = 5 and n(A ∩ B) = 2, find n(A ∪ B).
A universal set U has 10 elements and a set A has 4 elements. If A is a subset of U, what is n(A')?
If A = {1, 2, 3, 4, 5, 6} and B = {4, 5, 6, 7, 8, 9, 10}, what is A - B?
Sample Questions
Given A = {1, 2, 3, 4, 5} and B = {x : x ∈ N and x < 6}, which statement about these sets is correct after checking the elements one by one?
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A = B, A and B are equal sets, A and B are equivalent sets
A = {1, 2, 3, 4, 5}. The set B contains all natural numbers less than 6, so B = {1, 2, 3, 4, 5}. The two sets have identical elements, so they are equal. Equal sets always have the same number of elements, so they are also equivalent.
For sets A = {2, 5, 8, 11}, B = {2, 4, 6, 8} and C = {5, 6, 7, 8}, what is A ∪ (B ∩ C)?
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{2, 5, 6, 8, 11}
First find B ∩ C. The common elements are {6, 8}. Now take the union with A: {2, 5, 8, 11} ∪ {6, 8} = {2, 5, 6, 8, 11}.
For the same sets A = {2, 5, 8, 11}, B = {2, 4, 6, 8} and C = {5, 6, 7, 8}, what is (A ∪ B) ∩ (A ∪ C)?
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{2, 5, 6, 8, 11}
A ∪ B = {2, 4, 5, 6, 8, 11} and A ∪ C = {2, 5, 6, 7, 8, 11}. Their intersection is the common elements {2, 5, 6, 8, 11}.
A set P has 3 elements. How many subsets does P have, and how many proper subsets does P have?
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8 subsets, 7 proper subsets
For a set with n elements, number of subsets = 2^n and number of proper subsets = 2^n - 1. Here n = 3, so subsets = 2^3 = 8 and proper subsets = 8 - 1 = 7.
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