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Show that + : R xx R ->Rand xx : R xx R ...

Show that `+ : R xx R ->R`and `xx : R xx R ->R`are commutative binary operations, but ` - : RxxR ->R`and `-: : R_ *xxR_* ->R_*`are not commutative.

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`"Addition"`
Since,`a+b=b+a`
Hence, `+ " is a commutative binary operation"`


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NCERT ENGLISH-RELATIONS AND FUNCTIONS-SOLVED EXAMPLES
  1. Show that addition and multiplication are associative binary operatio...

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  2. Show that *: R xxR ->Rdefined by a*b = a +2bis not commutative.

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  3. Show that + : R xx R ->Rand xx : R xx R ->Rare commutative binary ope...

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  4. Let Y = {n^2: n in N} in N. Consider f : N ->Yas f(n)=n^2. Show tha...

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  5. Let f: N->R be a function defined as f(x)=4x^2+12 x+15. Show that f: N...

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  6. Consider f : N ->N, g : N ->Nand h : N ->Rdefined asf (x) = 2x, g (y) ...

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  7. Consider f:{1,\ 2,\ 3}->{a ,\ b ,\ c} and g:{a ,\ b ,\ c}-> {apple, ba...

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  8. Consider functions f and g such that composite gof is defined and is ...

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  9. Are f and g both necessarily onto, if gofis onto?

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  10. Let f : {1, 2, 3}->{a , b , c}be one-one and onto function given by f...

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  11. Let f"":""NvecY be a function defined as f""(x)""=""4x""+""3 , wher...

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  12. Let S = {1, 2, 3}. Determine whether the functions f : S->Sdefined as ...

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  13. Show that addition, subtraction and multiplication are binary operati...

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  14. Consider the identity function IN : N->N defined as, IN(x)=x for al...

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  15. Let R be a relation on the set A of ordered pairs of positive integer...

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  16. Let X={1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9} , Let R1 be a relation on X ...

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  17. Show that -ais not the inverse of a in Nfor the addition operation +...

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  18. If R1and R2are equivalence relations in a set A, show that R1nnR2is ...

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  19. Find the number of all one-one functions from set A = {1, 2, 3}to itse...

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  20. Let A={1,\ 2,\ 3} . Then, show that the number of relations containi...

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