Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9}. a. How many subsets of A are there? That is, find |P(A)|. b. How many subsets of A contain exactly 5 elements? c. How many subsets of A contain only even numbers? d. How many subsets of A contain an even number of elements?

a. What is P(A|B)? P(A and B)/P(B)=. b. What is P(B|A)? P(A and B)/P(A)= Are A and B independent? C. d. Are A and B mutually exclusive?

Consider the following set. {-5, -4, - . 0, 1, v2, 2, 2.5,4, 9} 0, 1, V2, 2, 2.5, 4, 9 Which numbers are even integers? (Select all that apply.) O -5 -4 1 1 V 2 2.5 4 9.

Is {2,2}={2, {2} }? How many elements are in the set {a,a,a,a,a}? {x€N|xis greater than 10 and x is divisible by 3} {x€Z|x is prime and x is divisible by 2} {X c is eqaul to z| x squared = 4}

2. Write as the sum/difference of logs. Express powers as factors. [(x+2)7 In

MK18. Show that in any set of 9 integers chosen from the set {2,3, 4, ... , 21, 22}, there are at least two integers that have a common factor greater than 1.

Which of the following phrases describes an empty set? O Common factors of 5 and 9. Multiples of 2 less than 10 that are divisible by 5. Prime numbers divisible by 2. Perfect squares less than 10 that is divisible by 3.

II. Determine whether the integers in each of these sets are pairwise relativelyprime. Show your solutions. 6. 11, 15, 187. 14, 15, 228. 12, 17, 31, 37,519. 7, 9, 10, 1310. 14, 17, 85

TIuuctivery. 2. Pigeonhole Principle: a. Show that in any group of 50 or more people there are at least 5 of them with the same birth month. b. Show that in any set of 7 (not necessarily consecutive) integers, there are two with the same remainder when divided by 6. C. Show that in any group of six or more people there are either three mutual strangers or three mutual acquaintances.