Question

If Q1 is the set of all rational numbers other than 1 with the binary operation *defined by a*b =a+b for all a, b in Q1 then the identity in Q1 w.r.t.* is
(A)1
(B)0
(C)-1
(D)2

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

If Q - {1} is the set of all rational numbers other than 1 with the binary operation defined by a*b =a+b for all a, b in Q - {1} then the identity in Q - {1} w.r.t. is

(A)1

(B)0

(C)-1

(D)2

EVALUATION

Here it is given that Q - {1} is the set of all rational numbers other than 1 with the binary operation defined by a*b =a+b for all a, b in Q - {1}

Let e be the identity element

Then by the definition

a*e = e*a = a

Which gives

a + e = a

⇒e = 0

So 0 is the identity element

FINAL ANSWER

Hence the correct option is (B) 0

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