Question

If the sets A and B are defined as A = {(x, y) : y = $e^x$, x ∈ R};

B = {(x, y) : y = x, x ∈ R}, then

• A. B ⊆ A
• B. A ⊆ B
• C. A ∩ B = ∅
• D. A ∪ B = A

Answer 1

The correct option is C

A ∩ B = ∅

We have,
A = {(x, y) : y = $e^x$, x ∈ R};

B = {(x, y) : y = x, x ∈ R},

Since A ∩ B is the set of points of intersection of curves y = $e^x$ and y = x
$\Rightarrow e^x=x$
which is not true for any real value of x.

or we can see from the graph below, that y = $e^x$ and y = x do not meet for any x ∈ R

$\therefore$ A ∩ B = ∅ .