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The set {x : x² + 1 = 0} over the reals is empty, and for A = {1, 2, 3} and B = {3, 4, 5} the union is {1, 2, 3, 4, 5}, so this Class 11 sheet opens with the empty set and a union. The answers record {3, 4} and the singleton {1}.
Key Takeaways
The set {x : x² + 1 = 0, x real} is empty (Q1).
A ∪ B = {1, 2, 3, 4, 5} when A = {1, 2, 3} and B = {3, 4, 5} (Q2).
Q3 records {3, 4} among the answers.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.
Which of the following sets is the empty set?
(a) {x : x is a real number and x² + 1 = 0} (b) {x : x is a natural number less than 4} (c) {x : x is a prime number between 5 and 10} (d) {x : x is an integer and -2 < x < 2}
2.
If A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = ?
(a) {1, 2, 3, 4, 5} (b) {1, 2, 3} (c) {3} (d) {1, 2, 3, 5}
3.
If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then A ∩ B = ?
(a) {1, 2} (b) {3, 4} (c) {5, 6} (d) {1, 2, 5, 6}
4.
The set of even natural numbers {2, 4, 6, 8, ...} in set-builder form is:
(a) {x : x = 2n, n ∈ N} (b) {x : x = n + 2, n ∈ N} (c) {x : x = 2n + 1, n ∈ N} (d) {x : x = 2n + 3, n ∈ N}
5.
If A = {1, 2, 3} and B = {2, 3, 4}, then A - B (A minus B) = ?
(a) {1} (b) {4} (c) {1, 2, 3, 4} (d) {2, 3}
6.
If A = {a, b}, then the number of subsets of A is:
(a) 2 (b) 4 (c) 8 (d) 1
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.
Define a set and give one example of a set written in roster form.
8.
Write the set {x : x ∈ R and x² - 5x + 6 = 0} in roster form.
9.
If A = {1, 3, 5} and B = {2, 4, 6}, write A ∪ B and A ∩ B.
10.
If A = {1, 2, 3} and B = {3, 4, 5}, verify that n(A ∪ B) = n(A) + n(B) - n(A ∩ B).
11.
State De Morgan's laws for two sets A and B.
12.
If U = {1, 2, 3, ..., 10} and A = {1, 3, 5, 7, 9}, find the complement A′ of A.
13.
Write the power set of A = {a, b}.
14.
If A ⊂ B and B ⊂ C, what relation holds between A and C?
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.
In a class of 40 students, 25 like cricket, 20 like football and 10 like both. How many students like at least one of the two games?
16.
Out of 100 students, 60 passed in Mathematics, 50 in Science and 30 in both. How many students failed in both subjects?
17.
In a survey of 200 people, 120 read newspaper A, 90 read newspaper B and 40 read both. How many people read neither newspaper?
18.
A group of 50 persons went on a tour. 30 visited Goa, 25 visited Kerala and 15 visited both. How many persons visited neither place?
19.
If U = {1, 2, ..., 12}, A is the set of multiples of 3 and B is the set of multiples of 4, find n(A ∪ B).
20.
In a class of 60 students, 35 play chess, 28 play carrom and 15 play both. Find the number of students who play neither chess nor carrom.
Answer Key
1. a) {x : x is a real number and x² + 1 = 0}
2. a) {1, 2, 3, 4, 5}
3. b) {3, 4}
4. a) {x : x = 2n, n ∈ N}
5. a) {1}
6. b) 4
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
Which of these sets is the empty set?
The set {x : x real and x² + 1 = 0}, option (a) in this worksheet (Q1).
What is A ∪ B when A = {1, 2, 3} and B = {3, 4, 5}?
{1, 2, 3, 4, 5}, option (a) in this worksheet (Q2).
What singleton set appears in the answer key?
{1}, option (a) in this worksheet (Q5).