Submission 1 (0.67/1 points) Friday, November 3, 2023 11:08 AM CDT Use the definitions of even, odd, prime, and composite numbers to justify your answers for (a)-(c). Assume that r and s are particular integers.
(a) Is 6rs even?
O Yes, because 6rs = 2(3rs) and 3rs is an integer.
O Yes, because 6rs = 2(3rs) + 1 and 3rs is an integer.
O No, because 6rs = 2(3rs) and 3rs is an integer.
O No, because 6rs = 2(3rs) + 1 and 3rs is an integer.
(b) Is 6r + 2s^2 + 3 odd?
O Yes, because 6r + 2s^2 + 3 = 2(3r + s^2 + 1) and 3r + s^2 + 1 is an integer. O Yes, because 6r + 2s^2 + 3 = 2(3r + s^2 + 1) + 1 and 3r + s^2 + 1 is an integer.
O No, because 6r + 2s^2 + 3 = 2(3r + s^2 + 1) and 3r + s^2 + 1 is an integer. O No, because 6r + 2s^2 + 3 = 2(3r + s^2 + 1) + 1 and 3r + s^2 + 1 is an integer.
(c) If r and s are both positive, is r^2 + 2rs + s^2 composite?
O Yes, because r^2 + 2rs + s^2 = (r + s)^2 and r + s is an integer
O Yes, because r^2 + 2rs + s^2 = (r + s)^2 and r + s is an integer
O No, because r^2 + 2rs + s^2 = (r + s) and r + s is not an integer.