Which sets of ordered pairs represent functions from A to B? (Select all that apply), and Explain how you've gotten your answer?
A = {a, b, c}
B = {8, 9, 10, 11}
(a,9)(b,10)(c,11)
To determine whether a set of ordered pairs represents a function from set A to set B, we need to ensure that each element in set A is paired with exactly one element in set B.
Let's consider each set of ordered pairs and check if it meets this condition:
1. {(a, 8), (b, 8), (c, 9), (c, 10)}:
Here, the element 'c' is paired with both 9 and 10, which violates the condition. Hence, this set does not represent a function from A to B.
2. {(a, 8), (b, 9), (c, 10)}:
In this set, each element in set A is paired with exactly one element in set B. Specifically, 'a' is paired with 8, 'b' is paired with 9, and 'c' is paired with 10. Thus, this set represents a function from A to B.
3. {(a, 11), (b, 9), (c, 11)}:
Here, 'a' and 'c' are both paired with 11, violating the condition of each element in A having exactly one corresponding element in B. Therefore, this set does not represent a function from A to B.
In conclusion, the second set of ordered pairs, {(a, 8), (b, 9), (c, 10)}, represents a function from A to B.
To determine which sets of ordered pairs represent functions from A to B, we need to make sure that for each element in A, there is a unique mapping to an element in B.
Let's go through the options:
1. {(a, 8), (b, 9), (c, 10), (a, 11)} - This set is not a function because it maps the element 'a' to both 8 and 11. Each element in A should have only one mapping.
2. {(a, 8), (b, 10), (c, 9)} - This set is a function because it correctly maps each element in A to a unique element in B without repeating any mappings.
3. {(a, 8), (b, 9), (c, 10), (c, 11)} - This set is not a function because it maps the element 'c' to both 10 and 11. Each element in A should have only one mapping.
Therefore, the set of ordered pairs that represent a function from A to B is option 2: {(a, 8), (b, 10), (c, 9)}.