Correct Option (4)
The problem defines p as a prime number and q as a composite number. We evaluate each statement:
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Statement 1: p × q can be an odd number.
For the product of two natural numbers to be odd, both numbers must be odd. Consider p = 3 (an odd prime number) and q = 9 (an odd composite number). Their product, p × q = 3 × 9 = 27, which is an odd number. Therefore, statement 1 is correct.
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Statement 2: q/p can be a prime number.
A composite number q can be formed by the product of two prime numbers. Let p = 29 (a prime number). If we choose q = 899, which is a composite number (since 899 = 29 × 31), then q/p = 899/29 = 31. Since 31 is a prime number, statement 2 is correct.
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Statement 3: p + q can be a prime number.
The sum of a prime number and a composite number can result in a prime number. Consider p = 5 (a prime number) and q = 6 (a composite number). Their sum, p + q = 5 + 6 = 11, which is a prime number. Therefore, statement 3 is correct.
Since all three statements (1, 2, and 3) are correct, the option that includes all of them is the correct answer.
Incorrect Options:
Options 1, 2, and 3 are incorrect because they do not include all the correct statements. As demonstrated above, statements 1, 2, and 3 are all factually correct based on the properties of prime and composite numbers.