Key Concepts in Computer Science Lab4 1- Suppose you wish to prove a theorem of the form "if x has property A then it has property B. (a) If you give a direct proof, what do you assume and what do you prove? (b) If you give an indirect proof (by contraposition), what do you assume and what do you prove? (c) If you give a proof by contradiction, what do you assume and what do you prove? 2- Use a proof by cases to show if x is an integer then x2+x is even. 3- Give a proof by contraposition (indirect proof) that if 3x2+2x+1 is odd, x is even. 4- Prove, by contradiction, that for all real numbers x and y if x not equal to y, x>0, and y>0, then x/y+y/x>2. 5- Prove, by contradiction, that for each real number x, if x is irrational then 3x is irrational