Sets, Relations...

R = {(1, 1), (2, 2), (1, 2), (2, 1), (2, 3)} be a relation on A = {1, 2, 3}, then R is

If R is a relation from a set A to a set B and S is a relation from B to C, then the relation  S  ^∘ R.

Let A be the set of all students of a boys school. The relation R in A given by R = {(a, b) : a is sister of b} is

The domain of definition of the function  

Let A = {1, 2, 3}. Which of the following is not an equivalence relation on A ?

The binary operation * defined on the set of integers as  a ∗b = |a −b|-1 is:

Let T be the set of all triangles in a plane with R a relation in T given by  R  = {(T₁ , T₂ ) : T₁  is congruent to  T₂ }. Then R is

The range of the function   

The function  f  (x) = x² + sin  x is

If A is a finite set containing n distinct elements, then the number of relations on A is equal to

R is a relation from { 11, 12, 13} to {8, 10, 12} defined by y = x –3. The relation  R⁻¹

 If A = {(1, 2, 3}, then the relation R = {(2, 3)} in A is

The range of the function f(x) = [sin x] is

The period of the function  f(x) = sin² x  + tan  x is