1. Ex. 2.5 # 18, 20. 24. . ?„. Prove that the product of a non-zero rational number and an irrational number is irrational. 3. Use a proof by cases to show that for any real numbers a. b and e. in...

1. Ex. 2.5 # 18, 20. 24.
. ?„. Prove that the product of a non-zero rational number and an irrational number is irrational.
3. Use a proof by cases to show that for any real numbers a. b and e. in in(a, rain(b, c)) = min(rttin(u, b). c).
4. Prove or disprove that if a and b are rational numbers then at is also rational. 5. Prove that given a real number x. there exist unique numbers 71 and c such that x = n c where 71 is an integer and 0