exercise 2.1 class 11
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NCERT Solutions class-11 Maths Exercise 2.1
Last Updated: May 17, 2016 by myCBSEguide
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Exercise 2.1
1. If find the values of and
Ans. Here
and
and
and
and
2. If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in (A B).
Ans. Number of elements in set A = 3 and Number of elements in set B = 3
Number of elements in A B = 3 3 = 9
3. If G = {7, 8} and H = {5, 4, 2}, find G H and H G.
Ans. Given: G = {7, 8} and H = {5, 4, 2}
GH = {(7, 5), (7, 4), (7, 2), (8, 5), (8, 4), (8, 2)}
And H G = {(5, 7), (4, 7), (2, 7), (5, 8), (4, 8), (2, 8)}
4. State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly:
(i) If P = and Q = then P Q =
(ii) If A and B are non-empty sets, then A B is a non-empty set of ordered pairs such that A and B.
(iii) If A = {1, 2}, B = {3, 4}, then
Ans. (i) Here P = and Q =
Number of elements in set P = 2 and Number of elements in set Q = 2
Number of elements in P Q = 2 2 = 4
But PQ = and here number of elements in P Q = 2
Therefore, statement is false.
(ii) True
(iii) True
5. If A = find A A A.
Ans. Here A =
A A =
A A A =
6. If A B = find A and B.
Ans. Given: A B =
A = set of first elements = and B = set of second elements =
7. Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that:
(i)
(ii) A C is a subset of B D.
Ans. Given: A = {1, 2}, B = {1, 2, 3, 4}, C
= {5, 6} and D = {5, 6, 7, 8}
(i) = {1, 2, 3, 4} {5, 6} =
……….(i)
A B = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4)}
A C = {(1, 5), (1, 6), (2, 5), (2, 6)
(AB) (A C) = ……….(ii)
Therefore, from eq. (i) and (ii),
= (A B) (A C)
(ii) A C = {(1, 5), (1, 6), (2, 5), (2, 6)
B D = {(1, 5), (1, 6), (1, 7), (1, 8), (2, 5), (2, 6), (2, 7), (2, 8), (3, 5), (3, 6), (3, 7), (3, 8),
(4, 5), (4, 6), (4, 7), (4, 8),
Therefore, it is clear that each element of A C is present in B D.
A C B D
8. Let A = {1, 2} and B = {3, 4}, write A B. How many sub sets will A B have? List them.
Ans. Given: A = {1, 2} and B = {3, 4}
A B = {(1, 3), (1, 4), (2, 3), (2, 4)}
Number of elements in A B = 4
Therefore, Number of subsets of AB = = 16
The subsets are:
{(1, 3)}, {(1, 4)}, {(2, 3)}, {(2, 4)}, {(1, 3), (1, 4)}, {(1, 3), (2, 3)}, {(1, 3), (2, 4)}, {(1, 4), (2, 3)}
{(1, 4), (2, 4)}, {(2, 3), (2, 4)}, {(1, 3), (1, 4), (2, 3)}, {(1, 3), (1, 4), (2, 4)}, {(1, 3), (2, 3), (2, 4)},
{(1, 3), (2, 3), (2, 4)}, {(1, 3), (1, 4), (2, 3), (2, 4)}
9. Let A and B be two sets such that and If are in A B.
Ans. Here
A and B
A and B
A and B
But it is given that and
A = and B = {1, 2}
10. The Cartesian Product A A has 9 elements among which are found and (0, 1). Find the set A and the remaining elements of A A.
Ans. Here
A and A
A and A
A
But it is given that which implies that
A =
And A A =
Therefore, the remaining elements of A A are
and