MCQs of Relations and Functions

Showing 21 to 30 out of 145 Questions

21.

f : [- \frac{π}{2}, \frac{π}{2}] \to [- 1, 1] i s a b i j e c t i o n i f_____

22.

f : R \to R, f (x) = x^{2} + 2 x + 3 i s_____

23.

If a ∗ b = ab+1 on R, is _____

(a)	commutative, but not associative
(b)	associative, but not commutative
(c)	neither commutative nor associative
(d)	both commutative and associative

24.

If a ∗ b = a²+b² on Z, then ∗ is _____

(a)	commutative and associative
(b)	commutative and not associative
(c)	not commutative and associative
(d)	nethier commutative nor associative

25.

I f a * b = a + b - a b o n Q - {1}, t h e n t h e i d e n t i t y a n d t h e i n v e r s e o f a f o r * a r e r e s p e c t i v e l y_____

26.

I f a * b = \frac{a b}{3} o n Q^{+}, t h e n 3 * (\frac{1}{5} * \frac{1}{2}) i s_____

27.

If ∆ is defined on P(X) (X≠ ∅) by, A ∆ B = (A ∪ B) - (A ∩ B), then _____

(a)	Identity for Δ is ø and inverse of A is A
(b)	Identity for Δ is A and inverse of A is ø
(c)	Identity for Δ is A' and inverse of A is A
(d)	Identity for Δ is X and inverse of A is ø

28.

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

29.

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.

30.

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

Showing 21 to 30 out of 145 Questions