Consider the following statements :

1. If f is the subset of Z × Z defined by f = {(xy, x − y); x, y ∈ Z}, then f is a function from Z to Z.

2. If f is the subset of N × N defined by f = {(xy, x + y); x, y ∈ N}, then f is a function from N to N.

Which of the statements given above is/are correct?

Consider the following statements :

1. The set of all irrational numbers between $\sqrt{2}$ and $\sqrt{5}$ is an infinite set.

2. The set of all odd integers less than 100 is a finite set.

Which of the statements given above is/are correct?

Let A = {7, 8, 9, 10, 11, 12, 13; 14, 15, 16} and let f ∶ A → N be defined by f(x) = the highest prime factor of x.

How many elements are there in the range of f?

Let R be a relation from N to N defined by R = {(x, y): x, y ∈ N and x2 = y³}. Which of the following are not correct?

1. (x, x) ∈ R for all x ∈ N

2. (x, y) ∈ R ⇒ (y, x) ∈ R

3. (x, y) ∈ R and (y, z) ∈ R ⇒ (x, z) ∈ R

Select the correct answer using the code given below :