Q. 54.2( 126 Votes )

# If A = {–1, 1}, find A × A × A.

Answer :

Given: A = {–1, 1}

cartesian product of a two sets A and B is given by set of multiplication of every member of the set with every other member of the set. Thus pairs of members of set are formed.

For given A,

A × A = {-1, 1} × {-1, 1}

A × A = {(-1, -1), (-1, 1), (1, -1), (1, 1)}

Now,

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)}

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

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