Discrete Mathematics Answers

Determine whether f is a function from the integers to the set of all real numbers.
Enter "Y" for yes and "N" for no.
1. f(n)=±n
2. f(n)=1/(n^2−16)
3. f(n)=√n^2+6
4. f(n)=1/(n^2+9)

Use Karnaugh map to minimize the sum of product expansion
xy'z+ xy'z'+x'yz+x'y'z+x'y'z'

Use Karnaugh map to minimize the sum of product expansion
xy'z+ xy'z'+x'yz+x'y'z+x'y'z'

WHAT IS THE CARDINALITY OF {a,{a},{a,{a}}}

In a a class of 80 students 53 study Art 60 study Biology 36 study art and Biology 34 study art and Chemistry 6 study Biology only and 18 study biology but not chemistry. How many students study art only and how many students study chemistry

Suppose that in the world every pair of people either
(a) likes one another,
(b) dislikes one another, or
(c) is indifferent toward one another.
Prove that in any gathering of 17 people, there is a group of three people all of whom satisfy one of conditions (a), (b) or (c).

Suppose a ϵ Z. Prove by contradiction that if a2 -2a + 7 is even, then a is even.

Use proof by contraposition to show that if x + y ≥ 2, where x and y are real numbers, then x ≥ 1 or y ≥ 1.

Suppose a ϵ Z. Prove by contradiction that if a2 -2a + 7 is even, then a is even.

If n is any even integer and m is any odd integer, then (n + 2)2 - (m - 1)2 is even.