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

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-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 ->R and xx : R xx R ->R are commutative binary ...

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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...

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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} ->{a p p l e ,...

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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 , where...

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

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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 R be a relation in X given by R1={(x,y)...

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

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  18. If R1 and R2 are equivalence relations in a set A, show that R1nnR2 i...

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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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