If A = {-1, 1},find A times A times A. | vedclass

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(A) It is known that for any non-empty set $A$,the Cartesian product $A 	imes A 	imes A$ is defined as the set of all ordered triples $(a, b, c)$ su

Vedclass · Accepted Answer

$A 	imes A 	imes A = \{(-1, -1, -1), (-1, -1, 1), (-1, 1, -1), (-1, 1, 1), (1, -1, -1), (1, -1, 1), (1, 1, -1), (1, 1, 1)\}$

Vedclass · Answer

(A) It is known that for any non-empty set $A$,the Cartesian product $A 	imes A 	imes A$ is defined as the set of all ordered triples $(a, b, c)$ such that $a, b, c \in A$.Given $A = \{-1, 1\}$.Therefore,$A 	imes A 	imes A = \{(a, b, c) : a, b, c \in \{-1, 1\} \}$.By taking all possible combinations of elements from $A$ for the three positions,we get:$A 	imes A 	imes A = \{(-1, -1, -1), (-1, -1, 1), (-1, 1, -1), (-1, 1, 1), (1, -1, -1), (1, -1, 1), (1, 1, -1), (1, 1, 1)\}$.

If $A = \{-1, 1\}$,find $A \times A \times A$.

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