Activity 2
Subject MATHEMATICS
Class XI
Chapter/Unit SUBSETS
Topic SETS
Time 40 minutes
Nature of Activity Individual
What will I learn? (Learning outcome)
To find the total number of subsets of a given set and verify that if a set has n number of
elements, then the total number of subsets is 2n.
Skills: - Visualizing, Creating, Accuracy, Precision
What do I require?
Hardboard, white thick sheets of paper, pencils, colours, a pair of scissors
coloured paper, felt tip or sketch pens, geometry box, glue stick,
What do I need to know?
Sets and its diagrammatical representation, Concepts on subsets of a set.
What do we have to do?
Calculation of number of subsets of a set
➢ Teacher’s activity
Teacher will explain the subsets of various sets
How will I proceed?
➢ Student’s activity
Student will
a. Using a sheet of paper and cut outs as shown, Take the empty set (say) U0 which has no
element.
b Take a set (say) U1 and using a coloured ring of paper, represent one element (say) a.
c. Take a set (say) U2 and represent two elements (say) a and b in it.
d. Take a set (say) U3 and with coloured cut outs represent three elements (say) a, b and c.
What have I observed?
1. Represent U0 in Fig. 2.1
FIG 2.1
Here the possible subsets of U0 is U0 itself only, represented symbolically by . The
number of subsets of U0 is 1 = 2 0
FIG 2.2
2. Represent U1 as in Fig. 2.2. Here the subsets
of U1 are , {a}. The number of subsets of
A1 is 2 = 21
3. Represent U2 as in Fig. 2.3
Here the subsets of U2 are , {a}, {b}, {a, b}. The number of subsets of U2 is 4 =22.
FIG 2.3
4. Represent U3 as in Fig. 2.4 Here the subsets of U3 are , {a}, {b}, {c), {a, b},
{b, c), {a, c) and {a, b, c}.
FIG 2.4
The number of subsets of U3 is 8 =23.
5. Going on this way, the number of subsets of set Un containing n
elements a1, a2, ..., an is 2n.
What have I learnt?
S. No. .
1 1. The number of subsets of U0 is 2−
2 The number of subsets of U1 is 2−
3 The number of subsets of U2 is 2−
4 The number of subsets of U3 is 2−
5 . The number of subsets of U10 is 2−
6 The number of subsets of Un is 2−
What have I learnt ?
The activity can be used for calculating the number of subsets of a given set.
Let me evaluate myself
Q1. Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express the following assets:
(i) n ∈ X but 2n ∉ X (ii) n + 5 = 8 (iii) n is greater than 4.
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Q2 . If X and Y are two sets and X′ denotes the complement of X, then X ∩ (X ∪ Y)′ is equal to
(a) X (b) Y (c) φ (d) X ∩ Y
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Q3. In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students
play both the games. Then, the number of students who play neither is
( a) 0 (b) 25 (c ) 35 ( d) 45
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Q4. Two sets A and B are such that n(A ∩ B) = 21, n(A ́ ∩B ́) = 9, n(A ∩ B) = 7
find n(A ∩B) ́.
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Q5. A survey shows that 63% people watch news channel A whereas 76% people watch news
channel B. If x% of people watch both news channels, then prove that 39 ≤ x ≤ 63.
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