Given that P is the set of all prime numbers between 0 and 10, and Q is the set of all odd numbers between 0…

Step 1: Analyze the Question

We are given two sets, $P$ and $Q$, defined within the range of 0 to 10. We need to find the symmetric difference between these two sets, which is represented by the union of $(P \setminus Q)$ and $(Q \setminus P)$.

Step 2: Define the Sets

• Set P (Prime numbers between 0 and 10): Prime numbers are numbers greater than 1 with only two factors (1 and itself). $P = \{2, 3, 5, 7\}$
• Set Q (Odd numbers between 0 and 10): Odd numbers are integers not divisible by 2. $Q = \{1, 3, 5, 7, 9\}$

Step 3: Solve Step-by-Step

1. Find elements in P that are not in Q ($P \setminus Q$): These are prime numbers that are not odd. Looking at $P = \{2, 3, 5, 7\}$ and $Q = \{1, 3, 5, 7, 9\}$, the only element in $P$ that is not in $Q$ is 2. $P \setminus Q = \{2\}$

2. Find elements in Q that are not in P ($Q \setminus P$): These are odd numbers that are not prime. Looking at $Q = \{1, 3, 5, 7, 9\}$ and $P = \{2, 3, 5, 7\}$, the elements in $Q$ that are not in $P$ are 1 and 9. $Q \setminus P = \{1, 9\}$

3. Find the union of these two results: Union means combining all unique elements from both sets. $\{2\} \cup \{1, 9\} = \{1, 2, 9\}$

Step 4: Identify the Answer

Comparing our result $\{1, 2, 9\}$ to the given options, it matches option D.

Exam Tip

When dealing with set operations like "elements in P not in Q" (relative complement), always list your sets clearly first. Remember that 1 is not a prime number, which is a common trap in JAMB questions. Checking your set definitions carefully before performing the operation will save you from silly mistakes!