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If R is a relation defined on set A = {1, 2, 3} such that R = {(1, 2), (2, 3)},

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Question: If R is a relation defined on set A = {1, 2, 3} such that R = {(1, 2), (2, 3)}, is R a function?

Options:

  1. Yes
  2. No
  3. Depends on A
  4. Not enough information

Correct Answer: No

Solution: 

A relation is a function if every element in the domain (set A) maps to exactly one element in the codomain. Here, 1 maps to 2, and 2 maps to 3, but 3 has no mapping, so R is not a function.

If R is a relation defined on set A = {1, 2, 3} such that R = {(1, 2), (2, 3)},

Practice Questions

Q1
If R is a relation defined on set A = {1, 2, 3} such that R = {(1, 2), (2, 3)}, is R a function?
  1. Yes
  2. No
  3. Depends on A
  4. Not enough information

Questions & Step-by-Step Solutions

If R is a relation defined on set A = {1, 2, 3} such that R = {(1, 2), (2, 3)}, is R a function?
Correct Answer: No, R is not a function.
  • Step 1: Identify the set A, which is {1, 2, 3}. This is the set of all possible inputs (domain).
  • Step 2: Look at the relation R, which is {(1, 2), (2, 3)}. This shows how elements from set A are paired with other elements.
  • Step 3: Check each element in set A to see if it has a mapping in R. The pairs in R show that 1 maps to 2 and 2 maps to 3.
  • Step 4: Notice that the element 3 in set A does not appear as a first element in any pair in R. This means 3 has no mapping.
  • Step 5: Conclude that for R to be a function, every element in set A must map to exactly one element. Since 3 does not map to anything, R is not a function.
  • Definition of a Function – A function is a relation where each element in the domain is associated with exactly one element in the codomain.
  • Domain and Codomain – Understanding the concepts of domain (input values) and codomain (output values) is crucial for determining if a relation is a function.
  • Mapping of Elements – Analyzing how each element in the domain maps to elements in the codomain helps in identifying functions.
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