Answer to Question #299854 in Discrete Mathematics for JEZ

Question

1.Specify the set A by listing its elements, where

A = {x: x is a whole number less than 100 and divisible by 16}.

2. Specify the set B in set-builder form by giving a written description of its elements,

where B = {0, 1, 4, 9, 16, 25}.

3. Consider

A = {m, a,t, h} C = {x: x = 3n, 1 ≤ n ≤ 4, n ∈ N}

B = {s,t, e, m} D = {x: x = 2n, 1 ≤ n ≤ 6, n ∈ N}

a. What is A ∩ B? b. What is C ∪ D?

5. Solve the following problem using a Venn diagram: Consider the following data

among 110 students in the college dormitory: 30 students are on a list A (taking

Accounting); 35 students are on a list B (taking Biology); and 20 students are on both

lists. Find the number of students:

a. on list A or B

b. on exactly one of the two lists

c. on neither list

Answer 1

Question 1

A = {x: x is a whole number less than 100 and divisible by 16}

 

The numbers less than 100 and divisible by 16 are;

16×0=0

16×1=16

16×2=32

16×3=48

16×4=64

16×5=80

16×6=96

A = { 0, 16, 32, 48, 64, 80, 96 } [Answer]

Question 2

B = {0, 1,  4, 9, 16, 25}

 

0, 1, 4, 9, 16, 25 are perfect square number.

 

Perfect square numbers are numbers that are a product of multiplying a number by itself.

1² =1×1=1 

2² =2×2=4

3² =3×3=9

4² =4×4=16

5² =5×5=25

 

B = { x: x is a perfect square number less than 30} [Answer]

Question 3

A = {m, a, t, h}

B = {s, t, e, m}

 

a) A∩C

A∩C are the elements that are common to set A and B 

 

A = {m, a, t,

h}

B = {s, t, e, m}

The elements that are common to A and B are m

and t

 

 

A∩B={m,t} [Answer]

 

b) C∪D

C∪D are the elements of C combined with the elements of D

C={x:x=3n,1≤n≤4,nϵN}

D={x:x=2n,1≤n≤6,nϵN}

 

 

C={x:x=3n,1≤n≤4,nϵN}

1≤n≤4,n=1,2,3,4

3n=3(1)=3

3n=3(2)=6

3n=3(3)=9

3n=3(4)=12

C={3,6,9,12}

 

 

D={x:x=2n,1≤n≤6,nϵN}

1≤n≤6,n=1,2,3,4,5,6

2n=2(1)=2

2n=2(2)=4

2n=2(3)=6

2n=2(4)=8

2n=2(5)=10

2n=2(6)=12

D={2,4,6,8,10,12}

 

C∪D={2,3,4,6,8,9,10,12} [Answer]

Question 5

Illustration

5a. on list A or B

10+20+15 = 45 [Answer]

5b. on exactly one of the two lists

10+15 = 25

5c. on neither list

110-45 = 65 [Answer]