Question

(i) A X B and (ii) A X A when A = {m,n) and B = 0.​

Answer 1

Answer:

If A and B are two non-empty sets, then the set of all ordered pairs (a, b) such that a ∈ A, b ∈ B is called the Cartesian Product of A and B, and is denoted by A x B .

Thus, A x B = { (a,b) |a ∈ A,b ∈ B }

A x B is the set of all possible ordered pairs between the elements of A and B such that the first coordinate is an element of A and the second coordinate is an element of B.

B x A is the set of all possible ordered pairs between the elements of A and B such that the first coordinate is an element of B and the second coordinate is an element of A.

If a = b, then (a, b) = (b, a).

The 'Cartesian Product' is also referred as 'Cross Product'.

In general

AxB ≠ BxA,

But,

n(A x B) = n(B x A)

AxB = ∅, if and only if A = ∅ or B = ∅.

If n(A) = p and n(B) = q ,then

n(AxB) = pq

Step-by-step explanation:

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