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Show that subtraction and division are n...

Show that subtraction and division are not binary operations on N.

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Let `a, b ∈ N`
For subtraction,
`a , b ∈ N ⇒ a − b ∉ N,` for `a=3` and `b=5`
`∴ ` Subtraction is not a binary operations on `N`. For division
...
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NCERT-RELATIONS AND FUNCTIONS-SOLVED EXAMPLES
  1. Let P be the set of all subsets of a given set X. Show that uu: P xx ...

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  2. Show that ∗ : RxxR->R given by (a ,b)->a+4b^2is a binary operation.

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  3. Show that subtraction and division are not binary operations on N.

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  4. Show that *: Rxx R ->Rgiven by a*b = a +2bis not associative.

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  5. Show that addition and multiplication are associative binary operatio...

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

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  7. Show that + : R xx R ->R and xx : R xx R ->R are commutative binary ...

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

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

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

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  11. Consider f : {1, 2, 3} ->{a , b , c}and g : {a , b , c} ->{a p p l e ,...

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

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

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

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

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

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

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

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

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  20. 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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