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?
Yes
No
Depends on A
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.
