2. Prove (using direct proof): If 3 a-1 is even, then is odd. Warning: Do not use fractions.
P: 3 a - 1 is even.
Q: is odd.
Proof. Assume that 3a - 1 is even. Then 3a - 1 = 2k for some integer k. Now,

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2. Prove (using direct proof): If 3 a-1 is even, then  is odd. Warning: Do not use fractions.
P: 3 a - 1 is even.
Q:  is odd.
Proof. Assume that 3a - 1 is even. Then 3a - 1 = 2k for some integer k. Now,

2. Prove (using direct proof): If 3 a-1 is even, then is odd. Warning: Do not use fractions.

P: 3 a - 1 is even.

Q: is odd.

Proof. Assume that 3a - 1 is even. Then 3a - 1 = 2k for some integer k. Now,

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2. Prove (using direct proof): If 3 a-1 is even, then is odd. Warning: Do not use fractions. P: 3 a - 1 is even. Q: is odd. Proof. Assume that 3a - 1 is even. Then 3a - 1 = 2k for some integer k. Now,

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2. Prove (using direct proof): If 3 a-1 is even, then is odd. Warning: Do not use fractions.

P: 3 a - 1 is even.

Q: is odd.

Proof. Assume that 3a - 1 is even. Then 3a - 1 = 2k for some integer k. Now,