Define a Cartesian product of two sets.

1.	Define a Cartesian product of two sets.
Answer» Let A and B two non-empty sets. Then, the Cartesian product of A and B is the set denoted by Ax B, consisting of all ordered pairs (a, b) such that a e A and be B. A x B= {(a, b): a ∈ A, b∈B} Keen Eye: If n(A) = p and n(B) = q, then n (A x B) = pq and n (B x A) = pq If at least one of A and B is infinite then AxB is infinite and B x A is infinite, In general, A x B ≠ B x A A x A x A = {(a, b, c) : a, b, c ∈A}. Here (a, b, c) is called an ordered triplet.

Answer»

Let A and B two non-empty sets. Then, the Cartesian product of A and B is the set denoted by Ax B, consisting of all ordered pairs (a, b) such that a e A and be B.

A x B= {(a, b): a ∈ A, b∈B}

Keen Eye:

If n(A) = p and n(B) = q, then n (A x B) = pq and n (B x A) = pq
If at least one of A and B is infinite then AxB is infinite and B x A is infinite,
In general, A x B ≠ B x A
A x A x A = {(a, b, c) : a, b, c ∈A}. Here (a, b, c) is called an ordered triplet.

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Define a Cartesian product of two sets.

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