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Class 12MathematicsRelations and FunctionsBinary operationsMedium
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On (A={1,2,3,4,6,12}), (a*b) is the greatest common divisor of (a) and (b). What is the identity element?

Answer and explanation

Correct answer: (12)

Step 1: For identity (e), (\gcd(a,e)=a) must hold for every (a \in A). Step 2: This happens for (e=12), because all elements of (A) divide (12). Step 3: For a GCD operation on divisors of a number, the largest element is often the identity.

Related tags

Binary OperationsGcdIdentityRelations And FunctionsMathematicsClass 12 Mcq
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10 more MCQs
  1. 1What is the correct meaning of a binary operation on a set (A)?
  2. 2If (a,b\in A) implies (a*b\in A), which property does this show?
  3. 3Why is usual addition (+) a binary operation on the set of natural numbers (\mathbb{N})?
  4. 4Why is usual subtraction (-) not a binary operation on the set of natural numbers (\mathbb{N})?
  5. 5How is usual multiplication (\times) on the set of integers (\mathbb{Z})?
  6. 6Why is usual division (\div) not a binary operation on the set of integers (\mathbb{Z})?
  7. 7If (a*b=a+b) is defined on real numbers, what type of operation is it?
  8. 8If (a*b=a-b) is defined on real numbers, which statement is correct?
  9. 9On real numbers, (a*b=a+b+1). What is the identity element of this operation?
  10. 10On real numbers, (a*b=a+b+ab). Which is the identity element of this operation?
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