Mathematics
Equal sets and Subsets
Practice questions
If A ⊆ B and B − A = ∅, which conclusion follows?If A = {x : x is a positive multiple of 4 less than 20}, which set is equal to A?If A is the set of prime divisors of 30, which of the following is a proper subset of A?If A = {x ∈ Z | x² = 16} and B = {−4, 4}, which statement is true?If A = {1, {2}, 3}, which statement is true?If A = {1, 2} and B = {1, 2, {1, 2}}, which statement is correct?If A and B are finite sets, A is a proper subset of B, and n(A) = 6, which value of n(B) is impossible?If A ⊆ B, n(A) = 4, n(B) = 4, and both sets are finite, which statement is correct?Let A = {x ∈ N : x is a divisor of 10} = {1, 2, 5, 10}. Which of the following is not a subset of A?Assertion: ∅ ⊆ A is true for every set A. Reason: There is no element in ∅ that is not in A. Choose the correct option.Assertion: If A = B, then A ⊆ B. Reason: Equal sets have exactly the same elements. Choose the correct option.Assertion: If n(A) = n(B), then A = B. Reason: Equal cardinality always gives identical elements. Choose the correct option.If A = {1, 2, 3, 4}, how many subsets have an even sum of elements?If A = {1, 2, 3}, how many ordered pairs (X, Y) satisfy X ⊆ A, Y ⊆ A, and X ⊆ Y?If A = {x : x ∈ N and x is a divisor of 18} and B = {1, 2, 3, 6, 9, 18}, what is the correct relation?If A = {1, 2, 3, 4, 5}, how many subsets contain 2 and do not contain 4?If U is the set of all students in a school and A is the set of Class 11 students, what does A′ represent?If A = {a, b, c, d, e, f, g}, how many subsets of A contain exactly 6 elements?If A = {1,2,3,4,5,6}, how many 4-element subsets of A contain both 1 and 2?If A ∩ B = A, which relation between A and B is correct?