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Prove that **: R xx R to R defined as a...

Prove that `**: R xx R to R ` defined as `a ** b =a+2ab` is not commutative .

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Let `a,b in R `
`:. A**b =a+2b and b**a =b+2a`
`:. a**b ne ** a " "`(If a =2 and b=5 )
Therefore, `**` is not commutative .
Hence Proved.
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NAGEEN PRAKASHAN-RELATIONS AND FUNCTIONS -Miscellaneous Exercise
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  3. Let f: W ->Wbe defined as f(n) = n - 1, if is odd and f(n) = n + 1, i...

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  4. If f: R ->Ris defined by f(x) = x^2- 3x + 2, find f(f(x)).

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  5. Show that the function f: R rarr { x in R: -1 lt x lt 1 } defined by ...

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  6. Show that the function f: R->Rgiven by f(x)=x^3is injective.

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  7. Give examples of two functions f:" "N->Z" "a n dg:" "Z->Z such that o...

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  8. Given examples of two functions f:" "N ->N" "a n d""""""g:" "N->N such...

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  9. Given a non-empty set X, consider P(X) which is the set of all subs...

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  10. Given a non-empty set X, consider the binary operation *: P(X)xx P(X)...

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  11. Find the number of all onto functions from the set {1, 2, 3, , n)to ...

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  12. Let S = {a , b , c} a n d T = {1, 2, 3}. Find F^(-1)of the following ...

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  13. Consider the binary operations*: RxxR->R and o: RxxR->R defined as ...

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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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  17. LetA = {1, 2, 3}Then number of relations containing (1, 2) a n d (1, 3...

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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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