1. **Problem statement:** Re-examine the calculations for $n(J \cap V)$ and $n(R')$ given the sets defined over the months of the year. 2. **Step 1: Recall the sets:** - $J = \{\text{January, June, July}\}$ - $V = \{\text{January, April, August, October}\}$ - $R = \{\text{October, December}\}$ - $U$ is all 12 months. 3. **Step 2: Find $n(J \cap V)$ correctly.** - Intersection means elements in both $J$ and $V$. - $J \cap V = \{\text{January}\}$ since January is the only month starting with J and a vowel. - So, $n(J \cap V) = 1$ (this was correct initially). 4. **Step 3: Find $n(R')$ correctly.** - $R' = U \setminus R$ means all months not ending with R. - $R = \{\text{October, December}\}$ - Months ending with R are October and December only. - So, $R' = \{\text{January, February, March, April, May, June, July, August, September, November}\}$ - Count elements: $n(R') = 10$ (this was also correct initially). **Final answers confirmed:** - $n(J \cap V) = 1$ - $n(R') = 10$