Which of the following compound statement contains exclusive OR'
p : Student can take computer or physical education as their fourth subject with PCM
q : Sun rises or moon rises
r : An integer greater than 1 is prime or composite

Options

A. p only
B. q only
C. r only
D. All P,q and r

Answer

To determine which of the given compound statements contains an exclusive OR, we need to analyze each statement based on the definition of exclusive OR. Exclusive OR means that one statement can be true, or the other can be true, but both cannot be true at the same time.

Let's evaluate each statement one by one:

1. **Statement P**: "A student can take computer or physical education as their fourth subject with PCM."
- Here, the student can choose either computer or physical education, but not both. If the student takes computer, they cannot take physical education, and vice versa. Therefore, this statement satisfies the condition for exclusive OR.

2. **Statement Q**: "Sun rises or moon rises."
- In this case, the sun rises during the day, and the moon rises at night. Both cannot rise at the same time. Thus, this statement also satisfies the condition for exclusive OR.

3. **Statement R**: "An integer greater than 1 is prime or composite."
- An integer greater than 1 is either prime (only divisible by 1 and itself) or composite (having more than two factors). An integer cannot be both prime and composite at the same time. Therefore, this statement also satisfies the condition for exclusive OR.

Since all three statements (P, Q, and R) satisfy the condition of exclusive OR, we conclude that:

**Final Answer**: All three statements (P, Q, and R) contain exclusive OR.

---