Question

of 200 clock radios with digital tuners and/or cd players sold recently in a department store, 140 had digital tuners and 180 had cd players. how many radios had both digital tuners and cd players? 100 radios (marked wrong)

Explanation:

Step1: Define set formula

For two sets, the principle of inclusion-exclusion is:
$$n(A \cup B) = n(A) + n(B) - n(A \cap B)$$
Rearranged to solve for the intersection:
$$n(A \cap B) = n(A) + n(B) - n(A \cup B)$$

Step2: Substitute given values

Let $n(A \cup B)=200$ (total radios), $n(A)=140$ (digital tuners), $n(B)=180$ (CD players).
$$n(A \cap B) = 140 + 180 - 200$$

Step3: Calculate the result

$$n(A \cap B) = 320 - 200 = 120$$

Answer:

120 radios