Let n∈z. prove that x is odd if and only if 5x 4 is odd. include the following in your proof: identify the type of the above statement. what would you need to show to prove the statement? identify the hypothesis and the conclusion wherever required. give two examples to show that this scenario either does or does not work. what proof technique seems appropriate in this particular situation? why? give the proof with an explanation to each step.

Arandomized controlled trial is designed to evaluate the effect of metoprolol in patients with heart failure. while preparing for statistical analysis, the researcher reviews some common types of statistical errors. which of the following statements is true regarding a type i error in a clinical study? a. the study is not significantly powered to detect a true difference between study groups. bthe null hypothesis is true but is rejected in error. c. the null hypothesis is false but is accepted in error. d. type i error is also known as beta and is usually 0.1 or 0.2. e. type i error depends on the study's confidence interval.