Q6 of 41 Page 33

If A × B = {(a, x), (a, y), (b, x), (b, y)}. Find A and B.

Given: A × B = {(a, x), (a, y), (b, x), (b, y)}

By definition of Cartesian product of two non-empty Set P and Q:


P × Q = {(p, q): p Є P, q Є Q}


Hence, we see A = set of all first elements.


B = set of all second elements.


⇒ A = {a,b} and B = {x,y}.


More from this chapter

All 41 →
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 × Q = {(m, n), (n, m)}.


(ii) If A and B are non-empty sets, then A × B is a non-empty set of ordered pairs (x, y) such that x ∈ A and y ∈ B.


(iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ ϕ) = ϕ.

 5

If A = {–1, 1}, find A × A × A.

 7

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that

(i) A × (B ∩ C) = (A × B) ∩ (A × C). (ii) A × C is a subset of B × D.


(ii) A × C is a subset of B × D.

 8

Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.