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prove that a function f = {(x,2x+1) : x ...

prove that a function f = `{(x,2x+1) : x in N}` defined on the set of natural numbers NxxN is one - one function.

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Here f (x) = `2x+1`
Let x, y `in` N and
f(x) = f(y)
`rArr 2x +1 = 2y + 1 rArr 2x = 2y rArr x =y`
Therefore, f(x) = f(y) `rArr x = y` , where x, y `in` N
Therefore, functions is one-one. Hence Proved.
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NAGEEN PRAKASHAN-RELATIONS AND FUNCTIONS -Miscellaneous Exercise
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  14. Given a non -empty set X, let *:" "P(X)" "xx" "P(X) ->P(X) be defined ...

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  15. Define a binary operation * on the set A={0,1,2,3,4,5} as a*b=a+b (mod...

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