# sets and set notation 3 problems

• Dec 3rd 2006, 10:44 AM
Retiredyoung24@yahoo.com
sets and set notation 3 problems
1. Use set notation to list the elements for natural numbers divisible by 4

a. {4,44,444, ....}
b. {..,-8,-4, 0,4,8.....}
c. {4,8,12.....}
d. {1,2,3,4.....}

2. Which of the following is a subset of Z = {5,10,15,20,.....}

a. {-5,0,5}
b. {10,20...}
c. {2,4,6....}
d. {3,6,9...}

3. Find the cardinality of the set A = {the letters in the word MATH}

a. 4
b. {M,A,T,H}
c. {B,C,D,E,F,G,I,J,K,L,N,O,P,Q,R,S,U,V,W,X,Y,Z}
d. 0
• Dec 3rd 2006, 11:14 AM
ThePerfectHacker
Quote:

Originally Posted by Retiredyoung24@yahoo.com
1. Use set notation to list the elements for natural numbers divisible by 4

a. {4,44,444, ....}
b. {..,-8,-4, 0,4,8.....}
c. {4,8,12.....}
d. {1,2,3,4.....}

(c)
Because natural numbers as,
$
{0,1,2,3,...
}$

Of these (c) fits the condition though it should have included the element 0.

Quote:

2. Which of the following is a subset of Z = {5,10,15,20,.....}

a. {-5,0,5}
b. {10,20...}
c. {2,4,6....}
d. {3,6,9...}
(b) any element of form 10k is 5(2k) is also of form 5k.
Quote:

3. Find the cardinality of the set A = {the letters in the word MATH}

a. 4
b. {M,A,T,H}
c. {B,C,D,E,F,G,I,J,K,L,N,O,P,Q,R,S,U,V,W,X,Y,Z}
d. 0
Cardinality is NOT a set is is a number (finite or infinite) in this case 4.
• Dec 3rd 2006, 11:19 AM
topsquark
Quote:

Originally Posted by Retiredyoung24@yahoo.com
1. Use set notation to list the elements for natural numbers divisible by 4

a. {4,44,444, ....}
b. {..,-8,-4, 0,4,8.....}
c. {4,8,12.....}
d. {1,2,3,4.....}

The answer to this depends on who you talk to. For some $\mathbb{N} = \{1, 2, 3,... \}$ and for others $\mathbb{N} = \{0, 1, 2, 3,... \}$.

Presumably your book has the former for the definition of the set of natural numbers. So we can see that option a doesn't contain all natural numbers divisible by 4, b contains negative numbers, and d is just all natural numbers. So the answer is c.

Quote:

Originally Posted by Retiredyoung24@yahoo.com
2. Which of the following is a subset of Z = {5,10,15,20,.....}

a. {-5,0,5}
b. {10,20...}
c. {2,4,6....}
d. {3,6,9...}

A subset contains only elements of the set, but may not contain all of them. So a contains negative elements, and c and d contain elements that are not in Z. So the answer is b.

Quote:

Originally Posted by Retiredyoung24@yahoo.com
3. Find the cardinality of the set A = {the letters in the word MATH}

a. 4
b. {M,A,T,H}
c. {B,C,D,E,F,G,I,J,K,L,N,O,P,Q,R,S,U,V,W,X,Y,Z}
d. 0

The cardinality of a set with a finite number of elements is just the number of elements. This set has 4 elements, so the answer is a.

-Dan