Q2) Miscellaneous Exercise Class11th Chapter 1st SETS- Maths CBSE | CBSE Maths By Poonam Garg
Q2) Miscellaneous Exercise Class11th Chapter 1st SETS- Maths CBSE | CBSE Maths By Poonam Garg
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Sets and their Representations
In everyday life, we often speak of collections of objects of a particular kind, such as,a pack of cards, a crowd of people, a cricket team, etc. In mathematics also, we come across collections, for example, of natural numbers, points, prime numbers, etc. More specially, we examine the following collections:
(i) Odd natural numbers less than 10, i.e., 1, 3, 5, 7, 9
(ii) The rivers of India
(iii) The vowels in the English alphabet, namely, a, e, i, o, u
Miscellaneous Exercise on Chapter 1
1. Decide, among the following sets, which sets are subsets of one and another:
A = { x : x R and x satisfy x2 – 8x + 12 = 0 },
B = { 2, 4, 6 }, C = { 2, 4, 6, 8, . . . }, D = { 6 }.
2. In each of the following, determine whether the statement is true or false. If it is
true, prove it. If it is false, give an example.
(i) If x A and A B , then x B
(ii) If A B and B C , then A C
(iii) If A B and B C , then A C
(iv) If A B and B C , then A C
(v) If x A and A B , then x B
(vi) If A B and x B , then x A
3. Let A, B, and C be the sets such that A B = A C and A B = A C. Show
that B = C.
4. Show that the following four conditions are equivalent :
(i) A B(ii) A – B = (iii) A B = B (iv) A B = A
5. Show that if A B, then C – B C – A.
6. Assume that P ( A ) = P ( B ). Show that A = B
7. Is it true that for any sets A and B, P ( A ) P ( B ) = P ( A B )? Justify your answer.
8. Show that for any sets A and B,
A = ( A B ) ( A – B ) and A ( B – A ) = ( A B )
9. Using properties of sets, show that
(i) A ( A B ) = A ( ii) A ( A B ) = A.
10. Show that A B = A C need not imply B = C.
11. Let A and B be sets. If A X = B X = and A X = B X for some set
X, show that A = B.
(Hints A = A ( A X ) , B = B ( B X ) and use Distributive law )
12. Find sets A, B and C such that A B, B C and A C are non-empty
sets and A B C = .
Exercise Questions Links:
Q1) Miscellaneous Exercise Class11th Chapter 1st SETS- Maths CBSE | CBSE Maths By Poonam Garg • Q1) Miscellaneous Exercise Class11th Chap...
Q2) Miscellaneous Exercise Class11th Chapter 1st SETS- Maths CBSE | CBSE Maths By Poonam Garg • Q2) Miscellaneous Exercise Class11th Chapt...