← Back to topic
Vidaara.orgClass 11 · Mathematics
CodeVID-M11-01-SUB-01
Subsets, Intervals & Power Set — Assignment
Chapter: Sets
Topic: Subsets, Intervals and the Power Set
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.
The number of subsets of $\{1,2,3,4\}$ is:
  • A.$8$
  • B.$16$
  • C.$4$
  • D.$32$
2.
The number of proper subsets of a $3$-element set is:
  • A.$8$
  • B.$7$
  • C.$6$
  • D.$3$
3.
$\varnothing\subseteq A$ is:
  • A.always true
  • B.sometimes true
  • C.never true
  • D.only if $A=\varnothing$
4.
The interval $[a,b)$ represents:
  • A.$a\le x\le b$
  • B.$a< x< b$
  • C.$a\le x< b$
  • D.$a< x\le b$
5.
If $A=\{1,2\}$, then $n(P(A))=$
  • A.$2$
  • B.$3$
  • C.$4$
  • D.$1$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Write all subsets of $\{1,2\}$.
7.
Write $\{x:-3\le x<2\}$ as an interval.
8.
If $n(A)=5$, find $n(P(A))$.
9.
Is $\{1,2\}$ a proper subset of $\{1,2,3\}$?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Write the power set of $\{a,b,c\}$.
11.
Express $(-\infty,3]$ in set-builder form.
12.
If $A=\{1,2,3\}$, how many subsets contain the element $1$?
13.
Write $[2,7]$ in set-builder form.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
If $A=\{1,2,3,4\}$, write the power set $P(A)$ and state $n(P(A))$.
15.
Given $A=\{x:x\in\mathbb{N},\ x\le5\}$, list all $4$-element subsets of $A$ and count them.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $16$
  2. (B) $7$
  3. (A) always true
  4. (C) $a\le x< b$
  5. (C) $4$
Section B — Short Answer (2 marks)
  1. $\varnothing,\{1\},\{2\},\{1,2\}$.
  2. $[-3,2)$.
  3. $32$.
  4. Yes.
Section C — Short Answer (3 marks)
  1. $\{\varnothing,\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\}$.
  2. $\{x:x\le3\}$.
  3. $4$.
  4. $\{x:2\le x\le7\}$.
Section D — Long Answer (5 marks)
  1. $P(A)$ has all $16$ subsets; $n(P(A))=16$.
  2. $\{1,2,3,4\},\{1,2,3,5\},\{1,2,4,5\},\{1,3,4,5\},\{2,3,4,5\}$ — five subsets.
Generated by Vidaara.org · Assignment VID-M11-01-SUB-01 · vidaara.org