Correct Option (D)
All three statements are correct.
-
Statement 1: p−cp+c can be even
Consider a prime number p = 13 and a composite number c = 15. Then, p−cp+c=13−1513+15=−228=−14. Since -14 is an even number, the statement holds true. -
Statement 2: 2p + c can be odd
Consider a prime number p = 2 and a composite number c = 9. Then, 2p+c=2(2)+9=4+9=13. Since 13 is an odd number, the statement holds true. -
Statement 3: pc can be odd
For the product of two integers to be odd, both integers must be odd. Consider a prime number p = 3 and a composite number c = 9. Then, pc=3×9=27. Since 27 is an odd number, the statement holds true.
Incorrect Options:
Options (A), (B), and (C) are incorrect because they do not include all three statements as correct. As demonstrated above, statements 1, 2, and 3 are all possible under the given conditions for prime (p) and composite (c) numbers.