Assume our "universal set" is the set of all letters in the alphabet, and consider the following sets:

Question

M = {x | x is a letter in "mathematics"}

P= {xx is a letter in "probability"},

S = {x | x is a letter in "statistics"). Write each of the following (in roster notation. Keep in mind that when working with sets, we only list each element once.

(a) P

(B) S

(c) P n S

(d) (M u P u S)’

Answer 1

P = {a, b, i, l, o, p, r, t, y} <-- This set contains all unique elements (letters) in the word "probability"

S = {a, c, i, s, t} <-- This set contains all unique elements (letters) in the word "statistics"

P ∩ S = {a, i, t} <-- This set contains only elements (letters) that are contained in BOTH the words "probability" and "statistics"

(M ∪ P ∪ S)' = {a, b, c, e, h, i, l, m, o, p, r, s, t, y}' = {d, f, g, j, k, n, q, u, v, w, x, z} <-- This set contains only elements (letters) that are NOT found in either the words "mathematics", "probability", or "statistics"

Hope the answers and explanations helped!