Which is an example of a survey involving quantitative data?
a. the favorite food of each person
b. the number of cavities each person has had
c. the color of the walls in each person’s bedroom
d. the type of car that each person owns

B. the number of cavities each person has had

B. The number of cavities each person has.

Step-by-step explanation:

We are required to find the survey consisting of quantitative data.

'Quantitative data are measures of values and are expressed in numbers'.

Thus, the survey having the data in the form of numbers will be an example of an quantitative data.

From the options, we see that,

'The number of cavities each person has' will give the result in the form of numbers.

All others would not provide numbers as the data.

Hence, the correct example of an quantitative data is,

B. The number of cavities each person has.

Vacuous proof is used.

Step-by-step explanation:

Given:

Proposition p(n) :

"if n is a positive integer greater than 1, then n² > n"

To prove:

Prove the proposition p (0)

Solution:

Using the proposition p(n) the proposition p(0) becomes:

p(0) = "if 0 is a positive integer greater than 1, then 0² > 0"

The proposition that "0 is a positive integer greater than 1" is false

Since the premises "if 0 is a positive integer greater than 1" is false this means the overall proposition/ statement is true.

Thus this is the vacuous proof which states that:

if a premise p ("0 is a positive integer greater than 1") is false then the implication or conditional statement p->q ("if n is a positive integer greater than 1, then n² > n") is trivially true.

So in vacuous proof, the implication i.e."if n is a positive integer greater than 1, then n2 > n." is only true when the antecedent i.e. "0 is a positive integer greater than 1" cannot be satisfied.