Question:
Let \(A=\{1,2,3,4\}\) and \(R:A\to A\) be the relation defined by \(R=\{(1,1),(2,3),(3,4),(4,2)\}\). The correct statement is :
Let \(A=\{1,2,3,4\}\) and \(R:A\to A\) be the relation defined by \(R=\{(1,1),(2,3),(3,4),(4,2)\}\). The correct statement is :
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List the image of each element of A and check for repeats and for elements left out.
Updated On: Oct 31, 2026
- \(R\) does not have an inverse
- \(R\) is not a one to one function
- \(R\) is an onto function
- \(R\) is not a function
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The Correct Option is C
Solution and Explanation
R sends 1 → 1, 2 → 3, 3 → 4, 4 → 2. Every element of A has exactly one image, so R is a function.
The images 1, 3, 4, 2 are all different, so R is one-one.
The set of images is {1, 2, 3, 4} = A, so R is onto.
A bijection has an inverse, so options (1), (2), (4) are false.
Answer: (3) R is an onto function
The images 1, 3, 4, 2 are all different, so R is one-one.
The set of images is {1, 2, 3, 4} = A, so R is onto.
A bijection has an inverse, so options (1), (2), (4) are false.
Answer: (3) R is an onto function
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