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(Solved): Problem 3. [30 points] Recall that a rational number can be put in the form qp where p and q ...



Problem 3. \( \left[30\right. \) points] Recall that a rational number can be put in the form \( \frac{p}{q} \) where \( p \)

Problem 3. points] Recall that a rational number can be put in the form where and are integers and . Prove the following for any rational number, : a. [10 points] If is rational, then is rational b. [ 10 points] If is rational, then is rational c. [ 10 points] If is rational, then is rational Problem 4. [20 points] Consider the statement: For all integers and , if is odd, then is odd or is odd. a. [10 points] Prove the statement using a proof by contrapositive b. [10 points] Prove the statement using a proof by contradiction


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Problem 2We have to prove that if a is odd integer then 3a+1 is e
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