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Show that zero is the identity for addit...

Show that zero is the identity for addition on R and 1 is the identity for multiplication on R. But there is no identity element for the operations `- : RxxR->R`and `-:: R_*xxR_*->R_*dot`

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Verified by Experts

We know that
`a+0=a=0+a `
and `a × 1 = a = 1 × a ∀ a ∈ R`
`⇒ 0` is the additive identity and `1` is the multiplicative identity in `R.`
...
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NCERT-RELATIONS AND FUNCTIONS-SOLVED EXAMPLES
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  2. Show that – a is the inverse of a for the addition operation '+' on R ...

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  3. Show that zero is the identity for addition on R and 1 is the identit...

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  4. Show that the vv: R ->R given by (a , b)->m a x {a , b}and the ^^: R -...

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  5. Let P be the set of all subsets of a given set X. Show that uu: P xx ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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