Relations and F...

Let f(x) = px + q and g(x) = mx + n. Then f (g(x)) = g (f(x)) is equivalent to

Suppose A = {X| X ∈ N, -1 < X < 8} and B = {Y| Y ∈ N, -1 < Y < 1} then find A × B.

Let N be the set of natural numbers and f : N → N be a function given by f (x) = x + 1 ∀ x ∈ N. Which one of the following is correct?

Which of the following statements is/are true:

1. Subtraction on the set of all natural numbers is a binary operation.
2. Subtraction on the set of all integers is a binary operation

If A = {2, 4, 5}, B = {5, 9, 11} and R is the relation from A to B such that a R b ⇔ b = 2a + 1 then the inverse relation of R is

If * is a operation on A = {- 1, 1} such that a * b = ab ∀ a, b ∈ A then find the identity element of A with respect to operation * ?

If f(x): R → Z and f(x)  = [x], where [.] denotes smallest integer function and g(x): Z → (0,∞) and g(x) = 5^x  then find the value of g o f(1/2) ? Note that Z is the set of all the integral values.

The number of one-to-one functions from {1, 2, 3} to {1, 2, 3, 4, 5} is

Let S be the set of all persons living in Delhi. We say that x, y in S are related if they were born in Delhi on the same day. Which one of the following is correct?

If f: R → R is a function such that f(x) = [x], where [.] denotes greatest integer function then f(x) is a