Question

Question:-The Cartesian product Z × Z has 9 elements among which are found (-2, 0) and (0, 2). Find the set Z and also the remaining elements of Z × Z.

Answer 1

Hey there!!!!

If n(M) = p and n(N) = q

then n(M × N) = pq.

Now,

n (Z × Z) = n(Z) × n(Z)

But, it is given that, n(Z × Z) = 9

Therefore, n(Z) × n(Z) = 9

n(Z) = 3



Hope it helps you☺

Answer 2

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We know that,

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

From the given,

n(A × A) = 9

n(A) × n(A) = 9,

n(A) = 3 ……(i)

The ordered pairs (-1, 0) and (0, 1) are two of the nine elements of A × A.

Therefore, A × A = {(a, a) : a ∈ A}

Hence, -1, 0, 1 are the elemets of A. …..(ii)

From (i) and (ii),

A = {-1, 0, 1}

The remaining elements of set A × A are (-1, -1), (-1, 1), (0, -1), (0, 0), (1, -1), (1, 0) and (1, 1)

Hope it's Helpful.....:)