Answer:

Sure! I'd be happy to explain it to you.

In mathematics, the null set (also called the empty set) is a set that doesn't contain any elements. It's like an empty box with nothing inside.

Let's look at the options given:

(A) P = {x | x is an even prime number}

An even prime number is a number that is divisible only by 1 and itself and is also an even number. However, there are no even prime numbers, as the only even number that could be a prime number is 2. But 2 is not considered an even prime because it is the only even number that is prime. So, P would be the null set because it doesn't have any elements.

(B) Q = {x | x is the number of points of intersection of two non-parallel lines}

When two lines intersect, they meet at a specific point. But when we consider two non-parallel lines, they will always intersect at exactly one point. So, Q would not be the null set since it would contain the number 1, representing the intersection point.

(C) R = {x | x is a natural number, and 1 < x < 2}

In this case, we are looking for a natural number (a positive whole number) between 1 and 2. However, there are no natural numbers between 1 and 2 because the number 2 is not included. So, R would be the null set because it doesn't have any elements.

(D) S = {x | x^2 = 9, x is odd}

Here, we are looking for numbers that, when squared, equal 9, and the numbers are odd. The only numbers that satisfy these conditions are -3 and 3, as (-3)^2 = 9 and (3)^2 = 9. Therefore, S is not the null set because it contains both -3 and 3.

So, out of the given options, the null set is represented by (A) P = { }. It's the set that doesn't contain any elements.