Let \(p_{1}\) and \(p_{2}\) denote two arbitrary prime numbers. Which one of the following statements is correct for all values of \(p_{1}\) and \(p_{2}\)?
Answer
(B)
Explanation
The product \(p_{1}p_{2}\) is divisible by \(p_{1}\), which is neither 1 nor the product itself (because \(p_{2} \ge 2\)). So \(p_{1}p_{2}\) always has a third divisor and is never prime, even when \(p_{1} = p_{2}\). Statement B holds for all primes.
One counterexample rules out each other option:
- A: \(2 + 3 = 5\) is prime.
- C: \(3 + 5 + 1 = 9\) is not prime.
- D: \(3 \times 5 + 1 = 16\) is not prime.
Answer: B