Let R be a relation defined as xRy if and only if 2x + 3y = 20, where x, y ∈ N. How many elements of the form (x, y) are there in R?

Consider the following statements:

1. A function f : Z → Z, defined by f(x) = x + 1, is one-one as well as onto.

2. A function f : N → N, defined by f(x) = x + 1, is one-one but not onto.

Which of the above statements is/are correct?

Consider the following in respect of a complex number z:

1. $\rm {\overline{\left(z^{-1}\right)}}=(\bar{z})^{-1}$

2. zz^-1 = |z|²

Which of the above is/are correct?

1. The difference of Z and its conjugate is an imaginary number.

2. The sum of Z and its conjugate is a real number.