Discrete Mathematics Answers

Let R1 = {(1, 2), (2, 3), (3, 4)} and R2 = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3), (3, 4)} be relations from {1, 2, 3} to {1, 2, 3, 4}. Find R1 − R2

Solve the following recurrence relation

a) T(n)=T(n-1) +1,for n>2 and T(1)=1

If f(x)=(x+1)/x, x ≠ 0 and g(x)= 2x+3, find g°f(x)

Find the inverse function of (x+1)/x

Define a set of which both {1, 3, 4} and {0, 3, 5} are subsets. Find such a set with the smallest possible number of elements.

We form the union of a set with 5 elements and a set with 9 elements. Which of the following numbers can we get as the cardinality of the union: 4, 6, 9, 10, 14, 20?

What is the number of subsets of a set with n elements, containing a given element (when element becomes fixed, part of every subset)?

1. A college freshman must take a science course, a humanities course, and a mathematics course. If she may select any of 6 science courses, any of 4 humanities, and any of 4 mathematics courses, how many ways can she arrange her program?

2. The store at your school wants to stock sweatshirts that come in four sizes (small, medium, large, extra-large) and in two colors (red and white). How many different types of sweatshirts will the store have to stock?

3. Rysel received a new wardrobe consisting of 6 shirts, 4 pairs of pants, 2 skirts, and 3 pairs of shoes for her birthday. How many new outfits can she make?

•Determine whether (p ⇔ q) and (¬p ∨ q) ∧ (¬q ∨ p) are logically equivalent.

•Determine whether p ∧ (p ⇔ q) ∧ ¬q is a tautology, contradiction, neither.