Question

Determine the number of elements in the indicated set. At East Zone University (EZU) there are 429 students taking College Algebra or Calculus. 283 are taking College Algebra, 198 are taking Calculus, and 52 are taking both College Algebra and Calculus. How many are taking Algebra but not Calculus?

Answer 1

Answer:

$n_A = 283$

$n_C =198$

$n_{A \cup C}=429$

$n_{A \cap C}= 52$

And we want to find the number of students that are taking Algebra but not Calculus.

We can solve this problem with the figure attached.

So we want to find this number of elements P represent number of elements:

$P(A \cap C')$

And we can find this number of elements with this formula:

$P(A \cap C')= P(A) -P(A \cap C) = 283-52= 231$

And that represent the number of students that are taking Algebra but not Calculus.

Step-by-step explanation:

For this case we define the following notation:

A = represent the students taking College Algebra

C =  represent the students taking College Calculus

A U C= represent the students taking College algerba or Calculus

$A \cap B$ represent the students taking College and Calculus

From the information given we have this:

$n_A = 283$

$n_C =198$

$n_{A \cup C}=429$

$n_{A \cap C}= 52$

And we want to find the number of students that are taking Algebra but not Calculus.

We can solve this problem with the figure attached.

So we want to find this number of elements P represent number of elements:

$P(A \cap C')$

And we can find this number of elements with this formula:

$P(A \cap C')= P(A) -P(A \cap C) = 283-52= 231$

And that represent the number of students that are taking Algebra but not Calculus.