HomeAdvance Math Class 10 10. If A ⊆ B and C ⊆ D then show that A×C ⊆ B×D - Advance Math Class 10 - Exercise: 1.2 10. If A ⊆ B and C ⊆ D then show that A×C ⊆ B×D - Advance Math Class 10 - Exercise: 1.2 Follow Us Solution:let (a, b) be one element of A×C∴ ⇒ a Є A and b Є C⇒ a Є B and b Є D (since, A ⊆ B and C ⊆ D)⇒ (a, b) Є B×DTherefore, A ×C ⊆ B × D Exercise: 1.2 1. If A = {1, 3, 5} and B= {2, 4, -1} then find A×B and B×A . Find the number of elements in A×B and B×A.2. (a) If A = {-1, 3, 6} and B= {-3, 5} then find A×B and B×A. Also draw the graph of the Cartesian products.(b) If A= {2, 4}, B= {-1, 3, 7}, C={1, 0} then with the help of tree diagram find A×B, B×A and A×B×C.3. If A= {x, y, u, v} and B= {a, b, l, m} then find A×B and represent the Cartesian product by a coordination diagram.4. If A= {3, 5}, B= {1, 2, 4}, C= {3, 4, 6} then show that(i) A×(BUC) = (A×B) U (A×C)(ii) A×(BꓵC) = (A×B) ꓵ (A×C)5. For the set A= {x:x Є I and -2 < x < 4} and B= {y:y is a root of y2 – 9=0} draw the graph of A×B and find n(A×B)6. Draw the graphs of A×B and B×A on two separate coordinate planes for the set A={-3, 0, 3} and B= {-1, 1}7. (i) If A=ф and B={-1, 1} then determine the power set of A×B, B×A and B2(ii ) If A= {0} and B= {1} then determine the A×B and B×A. Also determine P(A×B) and P(B×A)8. If A= {2, 4} and B = {4, 2}, Can we write A×B = A2 and B×A= B2 ?9. If n(A) = 3 and two of the elements of A × A be (a, a), (b, c) then determine the sets A and A × A.10. If A ⊆ B and C ⊆ D then show that A×C ⊆ B×D11. If A×B= {(m, 1), (n, 3), (m, 3), (n, 1), (m, 2), (n, 2)}, then find A and B.12. If A and B be non-empty sets and A × B= A × C then show that B=C.13. A= {1, 2}, B= {1, 3, 2} and C= {4, 2, 1} then show that A2 = B2ꓵC214. If A={0, 1} then find A×A×A Tags: Advance Math Class 10 Advance Math Class 10 - Chapter 1 Advance Math Class 10 - Exercise: 1.2