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HW 832054 2revis

This document is a revision worksheet for Grade XI Mathematics focusing on set theory. It includes various problems related to set operations, subsets, and surveys involving sets. The worksheet aims to enhance understanding of set relationships and properties.

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thuberajwardhan
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31 views1 page

HW 832054 2revis

This document is a revision worksheet for Grade XI Mathematics focusing on set theory. It includes various problems related to set operations, subsets, and surveys involving sets. The worksheet aims to enhance understanding of set relationships and properties.

Uploaded by

thuberajwardhan
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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SETS

REVISION WORKSHEET – 01(B)


Name: Grade: XI
Subject: Mathematics Date:

1 If X = {4n − 3n − 1: n ∈ N} and Y = {9(n − 1): n ∈ N}, then prove that X ⊂ Y.


2 If sets A and B are defined as A = {(x, y): y = 1 , 0 ≠ x ∈ R} , B = {(x, y): y = −x, x ∈ R}, then find
x
A ∩ B.
3 If A = {a, {b}}, then find all subsets of A.
4 If A ⊂ B, B ⊂ C and C ⊂ A then prove that A = C.
5 If A and B are two sets, then find A ∩ (A ∪ B).
6 What is the total number of proper subsets of a set containing n elements?
7 Write the sets {1 , 2 , 3
,
4
,
5
,
6 7
, } in the set-builder form.
2 5 10 17 26 37 50
8 For any two sets A and B, prove that A ∪ B = A ∩ B ↔ A = B.
9 For any two sets A and B prove that: n(A ∩ B) = n(A) + n(B) − 𝑛(𝐴 ∪ 𝐵).
10 For three sets A,B and C, show that A ∩ B = A ∩ C need not imply B = C.
11 If X and Y are two sets such that n(X) = 45, n(X ∪ Y) = 76 and n(X ∩ Y) = 12, then find n (Y).
12 In a survey of 100 persons it was found that 28 read magazine A, 30 read magazine B, 42 read
magazines C, 8 read magazines A and B, 10 read magazines A and C, 5 read magazines B and C and
3 read all the three magazines. Find;
(i) How many persons read none of the three magazines?
(ii) How many persons read magazine C only?
13 In a survey it was found that 21 persons liked product P1, 26 liked product P2 and 29 liked product
P3. If 14 persons liked products P1 and P2; 12 persons liked products P3 and P1; 14 persons liked
products P2 and P3 and 8 liked all the three products, then find how many liked products P3 only.
14 In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak Bengali. How
many speak Hindi only? How many people can speak Bengali? How many people can speak both
Hindi and Bengali?

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