If the sets A and B are defined as A = {(x, y) : y = 1 x , 0 ≠ x ∈ R} B = {( x, y) : y = -x, x ∈ R}, then Options: A . &nbsp A ∩ B = A B . &nbsp A ∩ B = B C . &nbsp A ∩ B = ∅ D . &nbsp None of these

Answer: Option C : C Since y = 1 x , y = -x meet when -x = 1 x ⇒ x 2 = -1, which does not give any real value of x. Hence, A ∩ B = ∅.

If the sets A and B are defined as A = {(x, y) : y = 1x, 0 ≠

Question

If the sets A and B are defined as

A = {(x, y) : y = $\frac{1}{x}$ , 0 ≠ x ∈ R}

B = {(x, y) : y = -x, x ∈ R}, then

Options:

A . A ∩ B = A

B . A ∩ B = B

C . A ∩ B = ∅

D . None of these

Answer: Option C
:
C

Since y = $\frac{1}{x}$ , y = -x meet when -x = $\frac{1}{x}$ ⇒ $x^{2}$ = -1,

which does not give any real value of x.

Hence, A ∩ B = ∅.

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