Please solve everything

The Equation Editor Shortcuts table below lists the commands you may need to complete this homework. For more shortcuts, please reference Steve Jones' list from the Blackboard. Please fill in your name and save the file as CSC231_homework 4_YourName.docx. Type your answer under each question. 1. Use a directed proof to show that the product of two rational numbers is rational. 2. Prove by contrapositive that if a is an integer, and a22a+7 is even, then a is odd. 3. Prove by contradiction that 200 cannot be written as a sum of an odd integer and two even integers. 4. Prove by contradiction that if x is a real number and x2+5x