Q5 of 41 Page 33

If A = {–1, 1}, find A × A × A.

Given: A = {–1, 1}

By definition A × A × A = {(a,b,c) : a,b,c Є A}.


⇒ A × A × 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)}


More from this chapter

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3

If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.

 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.

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

 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.