Question

If 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 ∩ B = A

• A ∩ B = B

• A ∩ B = Φ

• A ∪ B = A

Answer 1

If sets A and B are defined as A = `{(x, y) | y = 1/x, 0 ≠ x ∈ "R"}` B = {(x, y) | y = – x, x ∈ R}, then A ∩ B = Φ.

Explanation:

Given that, A = `{(x, y) | y = 1/x, 0 ≠ x ∈ "R"}`

And = {(x, y) | y = – x, x ∈ R}

It is very clear that y = `1/x` and y = – x

∵ `1/x ≠ - x`

∴ A ∩ B = Φ