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(ο) is a binary function such that aοb = a-b+1 where a,b∈z then the given binary function is
  • a)
    commutative and associative
  • b)
    commutative but not associative
  • c)
    associative but not commutative
  • d)
    neither associative nor commutative
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
(ο) is a binary function such that aοb = a-b+1 where a...
Explanation:

Commutative Property:
- For a binary function to be commutative, aοb should be equal to bοa for all a,b∈z.
- Let's check a simple case:
a=3, b=2
3ο2 = 3-2+1 = 2
2ο3 = 2-3+1 = 0
- Since 2 is not equal to 0, the function is not commutative.

Associative Property:
- For a binary function to be associative, (aοb)οc should be equal to aο(bοc) for all a,b,c∈z.
- Let's check a simple case:
a=1, b=2, c=3
(1ο2)ο3 = (1-2+1)-3+1 = -3
1ο(2ο3) = 1-(2-3+1)+1 = 3
- Since -3 is not equal to 3, the function is not associative.
Therefore, the given binary function is neither associative nor commutative, making the correct answer option 'D'.
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(ο) is a binary function such that aοb = a-b+1 where a,b∈z then the given binary function isa)commutative and associativeb)commutative but not associativec)associative but not commutatived)neither associative nor commutativeCorrect answer is option 'D'. Can you explain this answer?
Question Description
(ο) is a binary function such that aοb = a-b+1 where a,b∈z then the given binary function isa)commutative and associativeb)commutative but not associativec)associative but not commutatived)neither associative nor commutativeCorrect answer is option 'D'. 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 (ο) is a binary function such that aοb = a-b+1 where a,b∈z then the given binary function isa)commutative and associativeb)commutative but not associativec)associative but not commutatived)neither associative nor commutativeCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (ο) is a binary function such that aοb = a-b+1 where a,b∈z then the given binary function isa)commutative and associativeb)commutative but not associativec)associative but not commutatived)neither associative nor commutativeCorrect answer is option 'D'. Can you explain this answer?.
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