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Let '*' be the binary operation defined on the set Z of all the integers as
a * b = a + b + 1 for all a, b ∈ Z. The identity element w.r.t. this operation is
  • a)
    -1
  • b)
    -2
  • c)
    1
  • d)
    0
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Let * be the binary operation defined on the set Z of all the integers...
Identity Element in the Given Binary Operation
The identity element in a binary operation is an element that, when combined with any other element under that operation, gives the same element as the result. In other words, for any element 'a' in the set, the identity element 'e' satisfies the condition a * e = a.

Given Binary Operation *
In the given binary operation defined on the set Z of all integers as a * b = a + b + 1, we need to find the identity element.

Definition of Identity Element
Let's find the identity element 'e' such that a * e = a for all integers 'a'.
a * e = a + e + 1 = a
e = -1

Identifying the Identity Element
The identity element 'e' in this binary operation is -1, which satisfies the condition a * e = a for all integers 'a' in the set Z. Therefore, the correct answer is option 'A', which is -1.
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Let * be the binary operation defined on the set Z of all the integers asa * b = a + b + 1 for all a, b ∈ Z. The identity element w.r.t. this operation isa)-1b)-2c)1d)0Correct answer is option 'A'. Can you explain this answer?
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Let * be the binary operation defined on the set Z of all the integers asa * b = a + b + 1 for all a, b ∈ Z. The identity element w.r.t. this operation isa)-1b)-2c)1d)0Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let * be the binary operation defined on the set Z of all the integers asa * b = a + b + 1 for all a, b ∈ Z. The identity element w.r.t. this operation isa)-1b)-2c)1d)0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let * be the binary operation defined on the set Z of all the integers asa * b = a + b + 1 for all a, b ∈ Z. The identity element w.r.t. this operation isa)-1b)-2c)1d)0Correct answer is option 'A'. Can you explain this answer?.
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