26. Let E be the set of all even integers, and let O be the set of all odd integers. Let X = {n €Z|n = x +y for some a, y E O}. %3D (a) Prove that XCE. (b) Prove that EC X.

an Eulerian circuit an Eulerian path but no Eulerian circuit neither an Eulerian circuit nor an Eulerian

Using Richard Hammack's book of Elements of Discrete Mathematics chapter 18 in cardinality.   Briefly summarize Cantor’s argument of |N| ≠ |R|.

(a) How many injective functions are there from {1, 2, 3} to {1, 2, 3, 4, 5, 6, 7}? (b) How many subsets are there of {1, 2, 3, 4, 5, 6, 7} that are the range of an injective function with domain {1, 2, 3}? (c) What is the smallest number of people that must be in a group in order to guarantee that at least three people in the group were born in the same month (of possibly different years)? (The answer is not three; if you have three people they could all be born in the same month, but this is not guaranteed). (d) What is the coefficient of a a^5b^2 in (a + b)^7? (e) What is the coefficient of a^5b^2c in (a + b + c)^8?