THE GATEBOOK

Normalization Lectures

Let be one to one function.

S1:

S2:

Which of the following is TRUE?

(A). Only S1

(B). Only S2

(C), Both S1 and S2

(D). Neither S1 nor S2

Both S1 and S2 are true. Please note that this statements are true for any function. Function need not be one-one.

Let's assume but doesn't exist in

and also f(x) = y

So if y then x

but we are also stating that

this is only possible when x

So this is a contradiction

Hence we can say that S2 is true.

Note: Notice that y can only exist because of x because f is one to one

see this i have provided a counter example clearly functions is not one to one