Question

In a school there are a total of 20 teachers who can teach mathematics or physics. Of these, 12 can teach mathematics and 4 can teach both physics and mathematics. How many can teach physics?

• A. 16
• B. 8
• C. 12
• D. 6

Hint:

Math only = $12 - 4 = 8$. Total teachers ($20$) - Math only ($8$) = Physics ($12$).

Answer 1

The Correct Option is C

Step 1: Concept
Use the set theory formula: $n(M \cup P) = n(M) + n(P) - n(M \cap P)$.

Step 2: Analysis
Given: $n(M \cup P) = 20$, $n(M) = 12$, $n(M \cap P) = 4$.

Step 3: Calculation
$20 = 12 + n(P) - 4$
$20 = 8 + n(P)$
$n(P) = 12$.

Step 4: Conclusion
There are 12 teachers who can teach physics. Final Answer: (C)