Q8 of 65 Page 61

Let A = {1, 2} and B = {2, 3}. Then, write down all possible subsets of A × B.

Given: A = {1, 2} and B = {2, 3}


Need to write: All possible subsets of A × B


A = {1, 2} and B = {2, 3}


So, all the possible subsets of A × B are:


(A × B) = {(x, y): x A and y B}


= {(1, 2), (1, 3), (2,2), (2,3)}


More from this chapter

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6

If A and B be two sets such that n(A) = 3, n(B) = 4 and n(A ∩ B) = 2 then find.

(i) n(A × B)


(ii) n(B × A)


(iii) n(A × B) ∩ (B × A)


 7

For any two sets A and B, show that A × B and B × A have an element in common if and only if A and B have an element in common.

 9

Let A = {a, b, c, d}, B = {c, d, e} and C = {d, e, f, g}. Then verify each of the following identities:

(i) A × (B ∩ C) = (A × B) ∩ (A × C)


(ii) A × (B – C) = (A × B) – (A × C)


(iii) (A × B) ∩ (B × A) = (A ∩ B) × (A ∩ B)


 1

Let A and B be two nonempty sets.

(i) What do you mean by a relation from A to B?


(ii) What do you mean by the domain and range of a relation?