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Show that a is the inverse of a for th...

Show that a is the inverse of a for the addition operation + on R and `1/a`is the inverse of `a!=0`for the multiplication operation `xx` on R.

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Here (-a)+a=a+(-a)=0
Therefore, -a is the inverse of a for '+' operation.
Similarly , for , ` a in N,(1)/(a) in N,` if ` a ne 1`
Therefore , `(1)/(a)` can not be the inverse of 'a' for `'xx'` operation in N, if `a ne 1`
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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  16. Let A" "=" "{-1," "0," "1," "2} , B" "=" "{-4," "-2," "0," "2} and f,g...

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  18. Let A = {1, 2, 3}. Then number of equivalence relations containing (1...

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  19. Let f: R->Rbe the Signum Function defined as f(x)={1,x >0 0,x=0-1,x<1 ...

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