a. ? ⨁ ? = ? + ? + ?? b. ? ⊖ ? = ? + ? − 5
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. Find the identity element for the following binary operators defined on the set ℤ. If identity element exists then
find the inverse element also.
a. ? ⨁ ? = ? + ? + ??
b. ? ⊖ ? = ? + ? − 5
a. ? ⨁ ? = ? + ? + ??
Let the identity element for the binary operators defined on the set ℤ be 'e'.
Let 'a' be any element of Z
Then a ⨁ e = e ⨁ a =a
a ⨁ e= a+e +ae =a
and
e ⨁ a= e + a+ ea =a
This imply e=0
So that a ⨁ 0= a +0 + a.0 =a= 0+ a + 0.a= 0 ⨁ a
So in this case identity element be 0
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