If R is a relation defined on set A = {1, 2, 3} such that R = {(1, 2), (2, 3)}, is R a function?
Practice Questions
1 question
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
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.
Questions & Step-by-step Solutions
1 item
Q
Q: If R is a relation defined on set A = {1, 2, 3} such that R = {(1, 2), (2, 3)}, is R a function?
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.
Steps: 5
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.
