2) A = Eriris rational number and pacas. A number Mis said to be an upperbound of A if as M for all. ac A. Define B = Eq: 9 rational number and upper bound for A3." is an q A) Show B is non-empty. B) Show B doesn't have a smallest element Chint 2 happen). 92=2, <2 or 22. Argue First two can't

Consider the list of numbers: 2n-1, where n first equals 2, then 3, 4, 5,6,…What is the smallest value of n for which 2n -1 is not a prime number.  Show all your work.

R) The following proot seems to show that 2-1. Place a check mark In the step In which the error occurs. Step 1: Let a =b Step 2: a - ab Multiply by Step 1 Step 2 a- - ab -h stract Step 4: (a-5)(a+h) - ba-h) Factor Step 3 Step 3 Step 4 (e-ka Ma- - Step 5: Divide by la-) Step 6: a+b=b Simplify Step 5 Step 6 Step 7: b+b=b Step 8: 2h = b Since a=b %3D Simplify Step 7 Step 8 Step 9: 2 =1 Divide by b Step 9

Use a proof by contradiction to show that the difference of any rational number and any irrational number is irrational.

1 is the only number that has just one positive divisor and we call it a unit. 1 divides every number. 3 is a number that has exactly two positive divisors. Its divisors are 1 and 3. A number with exactly two divisors is called a prime. 12 is a number with six divisors. Its divisors are 1,2,3,4,6,12. A number with more than two positive divisors is called composite. The smallest number that is a prime is The smallest number that is composite is There are primes that are less than 10. There are composites that are less than 10. The smallest prime greater than 50 is