Question

9-2: all 35 students in a class take biology or math or both. 29 of them take biology and 15 take math. how many of them are taking both biology and math at the same time?

Explanation:

Step1: Apply principle of inclusion-exclusion

Let $n(B)$ = number taking Biology, $n(M)$ = number taking Math, $n(B\cup M)$ = total students, $n(B\cap M)$ = number taking both. The formula is:
$$n(B\cup M) = n(B) + n(M) - n(B\cap M)$$

Step2: Rearrange to solve for $n(B\cap M)$

$$n(B\cap M) = n(B) + n(M) - n(B\cup M)$$

Step3: Substitute given values

$$n(B\cap M) = 29 + 15 - 35$$

Step4: Calculate the result

$$n(B\cap M) = 44 - 35 = 9$$

Answer:

9