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Let * be a binary operation on Z defined by a * b = a + b – 15 for a, b ∈ Z. The identity element in (Z, *) is

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Let * be a binary operation on Z defined by a * b = a + b – 15 for a, b ∈ Z. The identity element in (Z, *) is

(A) 5 

(B) 10 

(C) 15 

(D) 0 

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Correct Option :- (C) 15

Explanation :-

Let e be the identity element. 

∴ For a ∈ Z, a * e = a = e * a 

⇒ a + e – 15 = a = e + a – 15 

⇒ e – 15 = 0 ⇒ e = 15 ∈ Z 

∴ The identity element is 15. 

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