1.

Show that zero is the identity for addition on R and1 is the identity for multiplication on R. But there is no identity elementfor the operations `-: RxxR->R`and `-:: R_*xxR_*->R_*dot`

Answer» We know that a+0=a=0+a and ` axx1 =a=1xxa AA a in R `
`implies ` 0 is the additive identity and 1 is the multiplicative identity in R.
Now ,there is no element e in R such that
`a-e =a=e-a AA a in R `
`:.` For `- : R xx R to R `, there is no identity element in R.
Similarly, for `div : R xx R to R `, there is no identity element in R.
Hence Proved.


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