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Assertion (A): Function f: {1, 2, 3 } {a, b, c, d) is defined by f= {(1, a), (2, b), (3, c)} has no inverse.
Reason (R): Functions ‘/ ’ is not one-to-one.
Reason (R): Functions ‘/ ’ is not one-to-one.
- a)A and R are both correct, also R is the correct explanation of A.
- b)A and R are both correct, but R is not the correct explanation of A.
- c)A is correct but R is wrong.
- d)A is wrong but R is correct.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Assertion (A): Function f: {1, 2, 3 } {a, b, c, d) is defined by f= {(...
Since, the image of the each element of A is belonging to only one element in B. But d has no pre-image in A Therefore, function is one-one but not onto.
So, its inverse does not exist.
Most Upvoted Answer
Assertion (A): Function f: {1, 2, 3 } {a, b, c, d) is defined by f= {(...
A and R are both correct, and R is the correct explanation for A.
Explanation:
To have an inverse, a function must be both injective (one-to-one) and surjective (onto).
In this case, the function f is not injective because both 1 and 2 are mapped to different elements in the codomain. Specifically, 1 is mapped to 'a' and 2 is mapped to 'b'. Therefore, there are multiple inputs (1 and 2) that map to the same output ('a' and 'b'), violating the injective property.
Because f is not injective, it cannot have an inverse. Therefore, both A and R are correct, and R provides the correct explanation for A.
Explanation:
To have an inverse, a function must be both injective (one-to-one) and surjective (onto).
In this case, the function f is not injective because both 1 and 2 are mapped to different elements in the codomain. Specifically, 1 is mapped to 'a' and 2 is mapped to 'b'. Therefore, there are multiple inputs (1 and 2) that map to the same output ('a' and 'b'), violating the injective property.
Because f is not injective, it cannot have an inverse. Therefore, both A and R are correct, and R provides the correct explanation for A.
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Assertion (A): Function f: {1, 2, 3 } {a, b, c, d) is defined by f= {(1, a), (2, b), (3, c)} has no inverse.Reason (R): Functions ‘/ ’ is not one-to-one.a)A and R are both correct, also R is the correct explanation of A.b)A and R are both correct, but R is not the correct explanation of A.c)A is correct but R is wrong.d)A is wrong but R is correct.Correct answer is option 'A'. Can you explain this answer?
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Assertion (A): Function f: {1, 2, 3 } {a, b, c, d) is defined by f= {(1, a), (2, b), (3, c)} has no inverse.Reason (R): Functions ‘/ ’ is not one-to-one.a)A and R are both correct, also R is the correct explanation of A.b)A and R are both correct, but R is not the correct explanation of A.c)A is correct but R is wrong.d)A is wrong but R is correct.Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Assertion (A): Function f: {1, 2, 3 } {a, b, c, d) is defined by f= {(1, a), (2, b), (3, c)} has no inverse.Reason (R): Functions ‘/ ’ is not one-to-one.a)A and R are both correct, also R is the correct explanation of A.b)A and R are both correct, but R is not the correct explanation of A.c)A is correct but R is wrong.d)A is wrong but R is correct.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): Function f: {1, 2, 3 } {a, b, c, d) is defined by f= {(1, a), (2, b), (3, c)} has no inverse.Reason (R): Functions ‘/ ’ is not one-to-one.a)A and R are both correct, also R is the correct explanation of A.b)A and R are both correct, but R is not the correct explanation of A.c)A is correct but R is wrong.d)A is wrong but R is correct.Correct answer is option 'A'. Can you explain this answer?.
Assertion (A): Function f: {1, 2, 3 } {a, b, c, d) is defined by f= {(1, a), (2, b), (3, c)} has no inverse.Reason (R): Functions ‘/ ’ is not one-to-one.a)A and R are both correct, also R is the correct explanation of A.b)A and R are both correct, but R is not the correct explanation of A.c)A is correct but R is wrong.d)A is wrong but R is correct.Correct answer is option 'A'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Assertion (A): Function f: {1, 2, 3 } {a, b, c, d) is defined by f= {(1, a), (2, b), (3, c)} has no inverse.Reason (R): Functions ‘/ ’ is not one-to-one.a)A and R are both correct, also R is the correct explanation of A.b)A and R are both correct, but R is not the correct explanation of A.c)A is correct but R is wrong.d)A is wrong but R is correct.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assertion (A): Function f: {1, 2, 3 } {a, b, c, d) is defined by f= {(1, a), (2, b), (3, c)} has no inverse.Reason (R): Functions ‘/ ’ is not one-to-one.a)A and R are both correct, also R is the correct explanation of A.b)A and R are both correct, but R is not the correct explanation of A.c)A is correct but R is wrong.d)A is wrong but R is correct.Correct answer is option 'A'. Can you explain this answer?.
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