Which of the following scenarios exhibits a function relation? take the first set listed to be the domain of the relation.
a. the set of tree heights and the set of trees in a forest
b. the set of car make and models and the set of people in a certain town
c. the set of birthdays and the set of students in a class
d. the set of people with social security cards and the set of social security numbers

Solution:

A relation is said to be function if for each member of domain there is unique value in range. And for no two different ranges values there should be a single domain member.

For, example , {(2,3), (4,6), (5,9),(0,7)} is a function.

But {(0,1),(0,2), (1,5),(3,6)} is not a function.

The set of first element of ordered pair is called Domain and the set of second elements of ordered pair is called range.

Option a: Take trees height found in forest as ,{1,2,3,4} and trees as, {A,B,C,D,E,F} as two trees can have same height means (1,A) and (1,E), so this can be a relation but not a function.

Option b: As, A same type and having same model car can be possessed by two different persons, so this can be relation but not a function.(C ,1),(C, 2)

Option c: As, on the same day that is single day , the birthday of two students can fall, so this can be relation but not a function.(12 January, Ran), (12 January, San)

Option d: As, different people having Social Security cards have different set of Social Security numbers. So this relation is a function.

People           Social Security numbers

A                          1

B                            2

AB                         12

C                              3

ABC                         123

True Option: d→→ the set of people with Social Security cards and the set of Social Security numbers

b

step-by-step explanation: