Home
Class 12
MATHS
Let f be a function from a set X to a se...

Let `f` be a function from a set X to a set Y. Consider the following statements
P : For each `x in X`, there exists unique `y in Y` such that `f(x) = y`.
Q : For each `y in Y`, there exists `x in X` such that `f(x) =y`.
R : There exist `x_1 , x_2 in X` such that `x_1 ne x_2 and f(x_1) = f(x_2)`.
The negation of the statement "f is one-to-one and onto" is

A

P or not R

B

R or not P

C

R or not Q

D

P and not R

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Similar Questions

Explore conceptually related problems

If f is real valued function such that f(x+y) = f(x) + f(y) and f(1) = 5 , then find the value of f(100)

If f is a function satisfying f(x+y)=f(x) . f(y) 'for all x, y in N such that f(1)=3 . And overset(n)sum_(x=1) f(x)=120 , find the value of n .

Check whether the following pair of statements are negation of each other. Give reasons for your answer. i) x+y=y+x is true for every real numbers x and y ii) There exists real numbers x and y for which x+y=y+x

Check whether the following pair of statements are negation of each other.Give reasons for your answer.(ii)There exists real numbers x and y for which x+y=y+x .

Check whether the following pair of statements are negation of each other Give reasons for your answer. i)x+y=y+x is true for every real number x and y. (ii)There exist a real number x and y for which x+y = y+x.

If S is a set with 10 elements and A= {(x,y):x, y in S, x ne y} , then the number of elements in A is

Let f(x) = (x+1)^2 -1, x ge -1 ). Then the set {x: f(x) = f^(-1) (x)} is

Let R be the set of all real numbers. If , f : R to R be a function such that |f (x) - f (y) | ^(2) le | x -y| ^(3), AA x, y in R, then f'(x) is equal to a)f (x) b)1 c)0 d) x ^(2)