Options C and D demonstrate that Tim's statement is incorrect, as both examples have odd and even numbers such that P + Q - 3 results in a prime number.
Tim's statement suggests that if P is an odd number and Q is an even number, then P + Q - 3 cannot be a prime number. Let's evaluate each option to show that Tim is incorrect:
A. 7 + 2 - 3 = 6
P = 7 (odd), Q = 2 (even)
P + Q - 3 = 7 + 2 - 3 = 6 (not a prime number)
B. 4 + 9 - 3 = 10
P = 4 (even), Q = 9 (odd)
P + Q - 3 = 4 + 9 - 3 = 10 (not a prime number)
C. 4 + 1 - 3 = 2
P = 4 (even), Q = 1 (odd)
P + Q - 3 = 4 + 1 - 3 = 2 (a prime number)
D. 1 + 4 - 3 = 2
P = 1 (odd), Q = 4 (even)
P + Q - 3 = 1 + 4 - 3 = 2 (a prime number)
Options C and D provide examples where P + Q - 3 is a prime number despite Tim's assertion. This disproves Tim's claim.