Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the set A = {x|x is an odd number less than 10} in roster form. {
Perfect! Roster form lists all elements explicitly.
(2) If A = {1, 2, 3}, is 4 ∈ A?
Correct! The symbol ∈ means "belongs to" or "is an element of".
(3) Write the cardinality of the power set of {a, b, c}.
Excellent! The power set includes all possible subsets.
(4) What is the number of subsets of a set with 4 elements?
Perfect! This includes the empty set and the set itself.
(5) Write an example of an infinite set using set-builder form.
Great! Set-builder notation describes the property that elements must satisfy.
Short Answer Questions (2 Marks Each)
Answer each question in 2-3 sentences
(1) Let A = {x : x is a natural number less than 7}, B = {x : x is a prime number less than 10}. Write A and B in roster form and find A ∩ B. A ∩ B (intersection): {
Excellent! Intersection contains elements common to both sets.
(2) Draw a Venn diagram to represent the following situation: A and B are two overlapping sets. Represent A ∩ B′.
A ∩ B′ represents: The part of set A that
Perfect understanding! B′ is the complement of B.
(3) If A = {2, 4, 6, 8}, B = {3, 6, 9}, find A ∪ B and A ∩ B.
A ∪ B (union): {
A ∩ B (intersection): {
Great! Union combines all elements, intersection finds common elements.
(4) Let U = {1, 2, 3, 4, 5, 6}, A = {2, 4, 6}. Find A′ (complement of A) with respect to U.
A′ = U - A = {
Correct! The complement contains all elements in U that are not in A.
(5) Find the number of elements in the power set of A = {p, q, r, s} and list any four subsets.
Number of elements in power set:
Excellent! Power sets include all possible combinations.
Long Answer Questions (4 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) Let A = {1, 2, 3}, B = {2, 3, 4}, C = {3, 4, 5}. Verify the identity: A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C).
A ∪ (B ∩ C): {
A ∪ B: {
A ∪ C: {
(A ∪ B) ∩ (A ∪ C): {
Perfect! This verifies the distributive property of union over intersection.
(2) Let A = {x ∈ N : x ≤ 10 and divisible by 2}, B = {x ∈ N : x ≤ 10 and divisible by 3}. Find A ∪ B, A ∩ B, and A – B.
A ∪ B: {
A ∩ B (multiples of 6): {
A – B (in A but not in B): {
Excellent work with set operations!
(3) A survey of 30 students showed that 18 liked Mathematics, 12 liked Science, and 8 liked both. Represent this information using a Venn diagram and find the required values.
(i) Students who like only Mathematics:
(ii) Students who like only Science:
(iii) Students who like both:
(iii) Students who like neither:
Perfect Venn diagram analysis!
(4) From the universal set U = {x ∈ N : x ≤ 20}, A = {multiples of 3}, B = {even numbers}. Find A ∩ B and A ∪ B.
A ∩ B (multiples of 6): {
A ∪ B: {
Excellent comprehensive analysis!
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) If A = {x ∈ N : x < 5}, then A =
(a) {0, 1, 2, 3, 4} (b) {1, 2, 3, 4} (c) {2, 3, 4, 5} (d) {1, 2, 3, 4, 5}
Correct! Natural numbers start from 1, and x < 5 means less than 5.
(2) The power set of a set with n elements contains:
(a) n elements (b) 2n elements (c)
Correct! The power set contains
(3) The number of subsets of A = {x, y, z, w} is:
(a) 8 (b) 12 (c) 16 (d) 20
Correct! For 4 elements:
(4) The Venn diagram that shows two disjoint sets A and B means:
(a) A ⊂ B (b) A ∩ B ≠ ∅ (c) A ∩ B = ∅ (d) B ⊂ A
Correct! Disjoint sets have no elements in common, so their intersection is empty.
(5) Which one is true for any set A?
(a) A ∪ A = ∅ (b) A ∩ A = ∅ (c) A ∪ A = A (d) A ∩ A = U
Correct! This is the idempotent property: A ∪ A = A and A ∩ A = A.
(6) If A = {1, 3, 5}, B = {2, 4, 6}, then A ∩ B =
(a) {1, 2} (b) {2, 3} (c) {5} (d) ∅
Correct! These sets have no common elements, so their intersection is empty.
(7) If a set has 3 elements, the power set will contain:
(a) 6 (b) 8 (c) 9 (d) 7
Correct! For 3 elements:
(8) Which of these is a subset of every set?
(a) {0} (b) {} (null set) (c) Universal set (d) {a}
Correct! The empty set (∅) is a subset of every set, including itself.
(9) If A = {a, b}, then P(A) =
(a) {{a}, {b}} (b) {∅, {a}, {b}, {a, b}} (c) {a, b, {a, b}} (d) {∅, a, b}
Correct! Power set includes all subsets: ∅, {a}, {b}, and {a, b}.
(10) If A = {x ∈ Z :
(a) {–3, –2, –1, 0, 1, 2, 3} (b) {–2, –1, 0, 1, 2} (c) {–3, 0, 3} (d) {–1, 0, 1}
Correct!
Sets Challenge
Determine whether these statements about sets are True or False: