a. Determine if the given statement is true or false. b. if the statement is a t
ID: 3028042 • Letter: A
Question
a. Determine if the given statement is true or false.
b. if the statement is a theorem, determine if the proof? is valid. If now correct the proof or construct a new, valid proof.
c. If the given statemtn is false, modify the statment to create a new statement which is true and also give a valid proof of the new statement.
16. Statement. Theorem? Proof? statement: Let m be an integer. Then m is even m2 is even. Proof? suppose m is an even integer. Then m 2k for some integer k. Therefore, 2(2k2). Since 2k is an integer, m is (2k)2 even. hat is if m is even, then m is even. 2e 1 for some integer (s Suppose m is an odd integer. Then m t Hence, m (2e 1)2 4 4e 2 2e) 1. Since (2 2e) is Thus, if m is odd, then m is odd. And the an inte is odd. is even contrapositive is if m2 is even, then mExplanation / Answer
a) Given statement is true
b) Given proofs are valid
First proof is by contrapositive
second proof is by contradiction
both the proofs are valid