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Give an example of a function from relation to relation that is 1.Onto but

Give an example of a function from relation to relation that is 1.Onto but not one-to-one 2.one-to-one but not onto 3.both onto and one-to-one (but different from the identity function).

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A)

1).Onto but not one-to-one

the function f:N→N defined by f(n)=n/2  is n is even

f(n)=n+/2 if n is odd

2) f(x) = x * 2

      Every distinct element of x has a different value of (x*2), thus
      the function is one-to-one. 

3)the function f:N→N defined by f(n)=n

 is both onto and one to one

 

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