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Consider the binary operation **:R xxR t...

Consider the binary operation `**:R xxR to R and o:R xx R to R` defined as `a**b = |a-b| and a o b = a `. For all `a , b in R`. Show that * is commutative but not associative, .o. is associative but not commutative.

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If S is a set of all rational numbers except 1 and ** be defined on S by a ** b = a + b-ab for all a, b in s then prove that ** is commutative as well as associative.

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SHARAM PUBLICATION-RELATIONS AND FUNCTIONS-EXAMPLE
  1. If S is the set of all rational numbers except 1 and * be defined on S...

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  2. Construct the multiplication table times7 on the set {1, 2, 3, 4, 5, 6...

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  3. Consider the binary operation **:R xxR to R and o:R xx R to R defined ...

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  4. Consider the binary operation **on the set {1, 2, 3 , 4, 5} defined by...

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  5. If ** is a binary operation on set Q of rational numbers such tht a**b...

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  6. if ** is the binary operation on N given by a**b= L. C. M of a and b. ...

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  7. if ** is the binary operation on N given by a**b= L. C. M of a and b. ...

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  8. Prove that f:X to Y is injective iff for all subsets A, B of X, f (A c...

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  9. Prove that f:X rarr Y is injective iff f^(-1) (f(A)) = "A for all" A s...

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  10. Prove that f:X rarr Y is surjective iff for all B sube Y, f(f^(-1)(B))...

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  11. Prove that for any f:X rarr Y , f o idx = f =idY of.

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  12. Let f: X rarr Y If there exists a map g:Y rarr X such that gof = id...

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  13. Let f:XrarrY. If there exists a map g:YrarrX such that g of=idxand fo ...

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  14. If ff(x)=cos[pi^2]x+cos[-pi^2]x where [x] stands for the greatest inte...

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  15. If f:RrarrR,g :RrarrR and h : RrarrR such that f(x)=x^2, g(x)= tan x a...

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  16. If p is a prime and ab-=0 (mod p) then show that either a=0 (mod p) or...

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  17. Prove that the relation R on the set Z of all integers defined by R={(...

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  18. Let n be positive integer and a function f be defined as f(n)={(0 , wh...

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  19. If f:RrarrR defined by f(x)=5x-8 for all x inR, then show that f is in...

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  20. Show that the inverse of a bijective function is unique.

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