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Which one of the following is false?
  • a)
    The set of all bijective functions on a finite setforms a group under function composition.
  • b)
    The set { 1 , 2 ,. . . , p - 1} forms a group under multiplication mod p where p is a prime number.
  • c)
    The set of all strings over a finite alphabet ∑ forms a group under concatenation.
  • d)
    A subset  of G is a subgroup of the group (G, *) if and only if for any pair of elements a, b ∈ s, a * b-1 ∈ s.
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Which one of the following is false?a)The set of all bijective functio...
In option (c), the set of all strings over a finite alphabet ∑ doesn’t forms a group under concatenation because the inverse of a string doesn’t exist with respect to concatenation.
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Which one of the following is false?a)The set of all bijective functions on a finite setforms a group under function composition.b)The set { 1 , 2 ,. . . , p - 1} forms a group under multiplication mod p where p is a prime number.c)The set of all strings over a finite alphabet ∑ forms a group under concatenation.d)A subsetof G is a subgroup of the group (G, *) if and only if for any pair of elements a, b ∈ s, a * b-1 ∈ s.Correct answer is option 'C'. Can you explain this answer?
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Which one of the following is false?a)The set of all bijective functions on a finite setforms a group under function composition.b)The set { 1 , 2 ,. . . , p - 1} forms a group under multiplication mod p where p is a prime number.c)The set of all strings over a finite alphabet ∑ forms a group under concatenation.d)A subsetof G is a subgroup of the group (G, *) if and only if for any pair of elements a, b ∈ s, a * b-1 ∈ s.Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Which one of the following is false?a)The set of all bijective functions on a finite setforms a group under function composition.b)The set { 1 , 2 ,. . . , p - 1} forms a group under multiplication mod p where p is a prime number.c)The set of all strings over a finite alphabet ∑ forms a group under concatenation.d)A subsetof G is a subgroup of the group (G, *) if and only if for any pair of elements a, b ∈ s, a * b-1 ∈ s.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which one of the following is false?a)The set of all bijective functions on a finite setforms a group under function composition.b)The set { 1 , 2 ,. . . , p - 1} forms a group under multiplication mod p where p is a prime number.c)The set of all strings over a finite alphabet ∑ forms a group under concatenation.d)A subsetof G is a subgroup of the group (G, *) if and only if for any pair of elements a, b ∈ s, a * b-1 ∈ s.Correct answer is option 'C'. Can you explain this answer?.
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