Question

If A = {(x, y) : y = sinx, x ∈ R} and B = {(x, y) : y = cos x, x ∈ R} then A ∩ B contains (1) no element (2) infinitely many elements (3) only one element (4) cannot be determined.

Answer 1

It will have infinitely many elements as for any x=2n (pi)+ pi/4 y will be 1/(2^(1/2))
where n is any natural no.

Answer 2

Concept:

To answer this question, we need to recall the concept of intersection of sets.

The intersection of two sets A and B is the set of all elements  which are common to both A and B. The symbol "∩" is used to denote the intersection.

Symbolically, A ∩ B = {x : x ∈ A and x ∈ B}.

Given:

The two sets are:

A = {(x, y) : y = sinx, x ∈ R} and B = {(x, y) : y = cos x, x ∈ R}

To find:

The intersection of set A and B.

Solution:

The range of sin x and cos x is [-1,1].

Since this interval contains infinite many real points.

then, The set A and B have infinite many points

and the common elements of both sets are infinite.

Hence,  A ∩ B  contains infinitely many points.

Option (2) is the correct choice.