2.1 set theory 宿題

Let U = {x | x is a letter of the alphabet} and V = {x | x is a vowel}. Decide whether each statement is true or false.

V’ ⊆ U

V ∈ U

∅ ⊆ V

{a, o u} = V

{f, p, q, w ,y} ⊆ V’

V’ ⊆ U True

V ∈ U False

∅ ⊆ V True

{a, o u} = V False

{f, p, q, w ,y} ⊆ V’ True

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}​, O = {1, 3, 5, 7, 9}​, E = { 0, 2, 4, 6, 8 }​, and T = { 4, 7, 8 }

Decide whether each statement below is true or false.

O ⊆ U

４ ∈ T
T ⊆ O

{0, 2, 4, 6, 8} = O’

O ⊆ U True

４ ∈ T True
T ⊆ O Fales

{0, 2, 4, 6, 8} = O’ True

Let U = { 6, 7, 8, 9, 10, 11, 12 } and C = { 7, 9, 11, 12 }.

List the members of the set C’.

C’ = { — }

​(Use a comma to separate answers as​needed.)

C’ = { 6, 8, 10 }

Decide whether the statement is true or false.

0 ⊆ ∅

A. False because ∅ is a​ set, so the expression should be written 0 ⊆ ∅.

B. False because ∅ represents a set with 0​ elements, not a set containing 0.

C. True because ∅ has 0 elements and 0 = 0.

D. True because ∅ is a set and 0 is a number.

B. False because ∅ represents a set with 0​ elements, not a set containing 0.

Let the universal set U be the set of​ integers, I​, and B = {x | x² ≤ 5, where x ∈ I}.

Write the elements of set B using the roster method.

​Note: I is an infinite set where

I = { ..., - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, ... }

B = {—-} (Use commas to separate the elements of the​ set)

B = {-2, -1, 0 1, 2}

Let S = { a, b, c, d, e,f, g}

a. How many subsets can be formed using the elements from set​ S?   

b. How many subsets can be formed using the elements from set S if each subset contains AT LEAST ONE ​element?   

a. 128 (2^7=128)

b. 127 (128-1=127)

A set contains fourteen elements.

a. How many subsets can be formed from this​ set?   

b. How many subsets containing exactly one element can be formed from the​ set?  

a. 16384 subsets

b. 14 subsets

Find the subsets of B = {a, f, j}

∅, {a}, {f}, {j}, {a, f}, {a, j}, {f, j}, {a, f, j}

Let set F = {13, 17, 21, 25}. Which of the sets​ below, written in​ set-builder notation, describes the elements of set F.

A. F = {y| y = 4x + 5, x∈ I, 1 ≤ x < 5}

B. F = {y| y = 4x + 5, x∈ I, 1 < x < 5}

C. F = {y| y = 4x + 5, x∈ I, 1 < x ≤ 5}

D. F = {y| y = 4x + 5, x∈ I, 1 ≤ x ≤ 5}

C. F = {y| y = 4x + 5, x∈ I, 1 < x ≤ 5}