MCQs of Relations and Functions

Showing 11 to 20 out of 98 Questions

11.

S is defined on N × N by ((a, b), (c, d)) ∈ S ⇔ a + d = b + c _____

(a)	S is reflexive, but not symmetric
(b)	S is Reflexive and transitive only
(c)	S is an equivalence relation
(d)	S is Transitive only

12.

Let S be the relation on the set A = {5, 6, 7, 8}, S = {(5, 6), (6, 6), (5, 5), (8, 8), (5, 7), (7, 7), (7, 6)}, then _____

(a)	S is reflexive and symmetric but not transitive
(b)	S is reflexive and transitive but not Symmetric
(c)	S is symmetric and transitive but not reflexive
(d)	S is an equivalence relation.

13.

I f f : R^{+} \to R, f (x) = \frac{x}{x + 1} i s_____

14.

I f f : R \to R, f (x) = [x], g : R \to R, g (x) = \sin x, h : R \to R, g (x) = 2 x, t h e n h o (g o f) =_____

15.

I f f : R \to (- 1, 1), f (x) = \frac{- x | x |}{1 + x^{2}}, t h e n f^{- 1} =_____

16.

f : R \to R, f (x) = \{\begin{matrix} - 1 \\ 0 \\ 1 \end{matrix} \begin{matrix} x < 0 \\ x = 0 \\ x > 0 \end{matrix} \begin{array}{l}  \end{array} g : R \to R, g (x) = 1 + x - [x], t h e n f o r a l l x, f (g (x)) =_____

17.

I f f : {x | x \geq 1, x \in R} \to {x | x \geq 2, x \in R}, f (x) = x + \frac{1}{x}, f^{- 1} (x) =_____

18.

I f f : R \to R, f (x) = x - [x], t h e n f^{- 1} (x) =_____

19.

f : R \to R, f (x) = x^{2}, g : R \to R, g (x) = 2^{x}, t h e n {x | (f o g) (x) = (g o f) (x)} =_____

20.

f : R \to Z, f (x) = [x] i s_____

(a)	one-one and onto and has an inverse
(b)	many-one and not onto, no inverse
(c)	many-one and onto, no inverse
(d)	one-one and not onto, no inverse

Showing 11 to 20 out of 98 Questions