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Given a domain of R, tell if it is a function

publish date: 2022/10/03 12:32:00 GMT+11

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Let A = {1, 2, 3, 4} and B = {2, 4, 5}

The following are all possible relations from A to B

R1 = {(1, 2), (1, 5), (2, 2), (3, 4), (3, 5), (4, 5)}
R2 = {(1, 4), (4, 2), (4, 5)}
R3 = {(3, 2), (3, 4), (3, 5), (1, 4)}
R4 = {(1, 4), (2, 5), (3, 2), (4, 4)}
R5 = {(1, 2), (2, 5), (3, 4), (4, 4)}

Which of these  relations represent a function

  • R1 (1) transparent a function
  • R2  (2) transparent a function
  • R3 (3) transparent a function
  • R4  (4) transparent a function
  • R5  (5) transparent a function
Please drag and drop the selected option in the right place or type it instead
represents
does not represent

Correct Answer

(1) does not represent
(2) does not represent
(3) does not represent
(4) represents
(5) represents

Explanation

  • The domain of R1 = {1, 2, 3, 4} = A. But there are two ordered pairs (1, 2) and (1, 5) in which the first element is same. Hence, R1 does not represent a function.
  • The domain of R2 = {1, 4} ≠ A. Also, there are two ordered pairs (4, 2) and (4, 5) in which the first element is the same. Hence, R2 is not a function, from A to B. Obviously, R3 is also not a function.
  • The domain of R4 = {1, 2, 3, 4} = A. And no two distinct pairs have the same first element. Hence, R4 represents a function. Similarly, R5 represents a function

Reference

Introduction to Differential Calculus (Systematic Studies with Engineering Applications for Beginners) - 2012

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