Q – 1 – If
find the values of x and y.
Solution:
Given:
This means;
Q  2  If the set A has 3 elements and the set B = {3,
4, 5}, then find the number of elements in (A x B)
Solution:
Here givenof elements in set A = 3]
n(B) = 3 [ number of elements in set B = 3]
Therefore,
n(A X B) = n(A) . n(B)
= 3 x 3
= 9
Hence, the number of elements in (A X B) = 9Hence, the number of elements in (A X B) = 9
Q – 3 – If G = {7, 8}, H = {5, 4, 2}, find G x H and H
x G.
Solution:
G = {7, 8} and H = {5, 4, 2} G X H = {7, 8} X {5, 4, 2}
= {(7, 5), (7, 4), (7, 2), (8, 5), (8, 4), (8, 2)}
H X G = {5, 4, 2} X {7, 8}
= {(5, 7), (5, 8), (4, 7), (4, 8), (2, 7), (2, 8)}
Q – 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 = {m, n} and Q = {n, m}, then P X Q = {(m, n), (n, m)}
Solution:) = 2 and n(Q) = 2
Therefore, n(P X Q) = 4, and here given n(PXQ) = 2,
Hence the given statement is false.
Now,
P X Q = {(m, n), (m, m), (n, n), (n, m)
(ii)If A and B are nonempty sets, the A x B is a nonempty set of ordered pairs (x, y)
such that
Solution:
False
Because if A and B are non empty sets, therefore, A X B is a nonempty set of ordered
pairs (x, y) such that
(iii) If A = {1, 2}, B = {3, 4}, then
Solution:
True
Q  5 If A = {1, 1}, find A x A x A.
Solution:
Given, A = {1, 1}
Therefore,
A x A x A = {(1, 1, 1), (1, 1, 1), (1, 1, 1), (1, 1, 1), (1, 1, 1), (1,1,1), (1, 1, 1), (1,1,1)}
Q  6 
Solution:
Q – 7 – Let A = {1,2}, B = {1 ,2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that
Solution:
Given,
Let A = {1,2}, B = {1 ,2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}
Therefore,
Hence,
Now,
A X B = {1, 2} x { 1, 2, 3, 4}
= {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4)}
And
A X C = {1, 2} x {5, 6}
= {(1, 5), (1, 6), (2, 5), (2, 6)}
Now,
Therefore, L.H.S. = R.H.S.
Hence,
(ii) A x C is a subset of B x D
Solution:
Given, Let A = {1,2}, B = {1 ,2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}
Therefore,
A x C = {1, 2} x {5, 6}
= {(1, 5), (1, 6), (2, 5), (2, 6)}
B x D = {1, 2, 3, 4} x {5, 6, 7, 8}
= {(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)}
As every element of Ax B is the element of B x D, so it is clear that
Ax B is a subset of B x D
Q – 8 – Let A = {1, 2} and B = {3, 4}. Write A x B. How many subsets will A x B have? List them.
Solution:
Given,
A = {1, 2} and B = {3, 4}
Therefore, A x B = {(1, 3), (1, 4), (2, 3), (2, 4)}
We know that number of subset having n element = 2^{n}.
In A x B, n = 4
Therefore subset of A x B = 2^{4} = 16
Hence,
A x B = {(1, 3), (1, 4), (2, 3), (2, 4)}
Number of subset in AxB = 16
Q – 9 – Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x,1) (y,2), (z,1) are in A x B, find A and B where x, y, and z are distinct elements.
Solution:
Given
n(A)=3 and n(B)=2
Therefore, n(AxB) = n(A)
n(B)= 3 x 2 = 6
Now, if (x,1) (y,2), (z,1) are in A x B,
Therefore, A = {x, y, z} and B ={1, 2}
Q – 10 – The Cartesian product A x A has 9 elements among which are found (1, 0) and (0, 1). Find the set A and the remaining elements of A x A.
Solution:
Given,
Cartesian product A x A has 9 elements among which are found (1, 0) and (0, 1)
This means A has 3 elements as (1,0)∈A×A and (0,1)∈A×A
Therefore, (1,0)∈A×A⇒1,0 ∈A
And (0,1)∈A×A⇒0,1 ∈A
Therefore, A={1,0,1}
Hence, rest elements of A×A={(1,1),(1,1),(0,1),(0,0),(1,1),(1,0),(1,1)
