Question

If the sets A and B are defined as A = {(x, y)|y = 1 / x, 0 ≠ x ∈ R}, B = {(x, y)|y = -x ∈ R} then
1. A ∩ B = ϕ 
2. A ∩ B = B
3. A ∩ B = A
4. None of these

Answer 1

Correct Answer - Option 1 : A ∩ B = ϕ 

Concept:

Set theory:

• A ∪ B means set of all the values in the set A and B.
• A ∩ B is the set of common elements of A and B.

 

Calculation:

Given sets:

A = {(x, y)|y = 1 / x, 0 ≠ x ∈ R} and B = {(x, y)|y = -x ∈ R}

For any value of x ∈ R and x ≠ 0;

In set A element will be (x, 1/x); and in set B will be (x, - x)

For A ∩ B; 

\(\rm \frac{1}{x} = -x\)

⇒ x² = -1

which is not possible for any x ∈ R

∴ A ∩ B = ϕ