Discrete Mathematics Answers

If n fair six-sided dice are tossed and the numbers showing on top are recorded, how many

(a) record sequences are possible?

(b) sequence contain exactly one six?

(c) sequences contain exactly four twos, assuming n >= 4 

If n fair six-sided dice are tossed and the numbers showing on top are recorded, how many

(a) record sequences are possible?

(b) sequence contain exactly one six?

(c) sequences contain exactly four twos, assuming n  4 ?

Draw De Morgan’s Law, Absorption and Complementation Laws

Let A = {m, n, o}, B = {a, b}, and C = {7, 2}. Find: a) A x B x C. b) C x B x A. c) C x A x B. d) B x B x B.

Determine whether these statements are true or false. a) ∅ ∈ {∅} b) ∅ ∈ {∅, {∅}} c) {∅} ∈ {∅} d) {∅} ∈ {{∅}} e) {∅} ⊂ {∅, {∅}} f ) {{∅}} ⊂ {∅, {∅}} g) {{∅}} ⊂ {{∅}, {∅}}

Suppose that A = {2, 4, 6}, B = {2, 6}, C = {4, 6}, and D = {4, 6, 8}. Determine which of these sets are subsets of which other of these sets.