1. **Problem statement:** In a class of 50 students, 20 are certified in Java, 15 are certified in SQL, and 5 are certified in both Java and SQL. We need to find how many students are certified neither in SQL nor Java. 2. **Formula used:** To find the number of students certified in either Java or SQL, we use the principle of inclusion-exclusion: $$|J \cup S| = |J| + |S| - |J \cap S|$$ where $|J|$ is the number certified in Java, $|S|$ is the number certified in SQL, and $|J \cap S|$ is the number certified in both. 3. **Calculate the number certified in Java or SQL:** $$|J \cup S| = 20 + 15 - 5 = 30$$ 4. **Calculate the number certified neither in Java nor SQL:** Total students = 50 $$\text{Neither} = 50 - |J \cup S| = 50 - 30 = 20$$ 5. **Answer:** 20 students are certified neither in SQL nor Java.