← Back to topic
Vidaara.orgClass 11 · Mathematics
CodeVID-M11-01-OPS-01
Operations on Sets — Assignment
Chapter: Sets
Topic: Operations on Sets and Venn Diagrams
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
$A\cap A'$ equals:
  • A.$A$
  • B.$U$
  • C.$\varnothing$
  • D.$A'$
2.
$A\cup U$ equals:
  • A.$A$
  • B.$U$
  • C.$\varnothing$
  • D.$A'$
3.
By De Morgan's law, $(A\cap B)'=$
  • A.$A'\cap B'$
  • B.$A'\cup B'$
  • C.$A\cup B$
  • D.$A-B$
4.
If $A\subseteq B$, then $A\cap B=$
  • A.$B$
  • B.$A$
  • C.$\varnothing$
  • D.$U$
5.
$n(A\cup B)$ equals:
  • A.$n(A)+n(B)$
  • B.$n(A)+n(B)-n(A\cap B)$
  • C.$n(A)-n(B)$
  • D.$n(A)\cdot n(B)$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $A=\{1,2,3\}$ and $B=\{3,4\}$, find $A\cup B$.
7.
For the same $A,B$, find $A\cap B$.
8.
For the same $A,B$, find $A-B$.
9.
If $n(A)=20,\ n(B)=15,\ n(A\cap B)=5$, find $n(A\cup B)$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
If $A=\{1,2,3,4\}$ and $B=\{3,4,5,6\}$, find $A-B$ and $B-A$.
11.
With $U=\{1,2,3,4,5,6\}$, $A=\{1,2,3\}$, $B=\{3,4\}$, verify $(A\cup B)'=A'\cap B'$.
12.
In a class of $35$, $24$ like tea and $20$ like coffee; each likes at least one. How many like both?
13.
If $A=\{x:x\in\mathbb{N},\ x\le6\}$ and $B=\{x:x\text{ even},\ x\le6\}$, find $A-B$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
In a survey of $60$ people, $25$ read paper A, $26$ read B, $26$ read C; $9$ read A & B, $11$ read B & C, $8$ read A & C, and $3$ read all three. How many read at least one paper?
15.
If $n(U)=50,\ n(A)=20,\ n(B)=28,\ n(A\cap B)=8$, find $n(A'\cap B')$.

Answer Key

Section A — Multiple Choice Questions
  1. (C) $\varnothing$
  2. (B) $U$
  3. (B) $A'\cup B'$
  4. (B) $A$
  5. (B) $n(A)+n(B)-n(A\cap B)$
Section B — Short Answer (2 marks)
  1. $\{1,2,3,4\}$.
  2. $\{3\}$.
  3. $\{1,2\}$.
  4. $30$.
Section C — Short Answer (3 marks)
  1. $A-B=\{1,2\}$, $B-A=\{5,6\}$.
  2. Both equal $\{5,6\}$.
  3. $9$.
  4. $\{1,3,5\}$.
Section D — Long Answer (5 marks)
  1. $52$.
  2. $10$.
Generated by Vidaara.org · Assignment VID-M11-01-OPS-01 · vidaara.org