Download section 1.1 solutions

Section 1.1 solutions
Homework #1 – 8. List all of the elements in the sets described below. Write your answer
using set braces.
1) The set A of even numbers between 1 and 10 inclusive.
My answer can only include numbers between 1 and 10. It is okay to include the endpoints
because of the word inclusive. However, 1 won’t be in my answer as 1 is not an even
number.
Here are the even numbers between 1 and 10 are: 2,4,6,8,10
10 is an end point and it is even. 10 will be part of my answer.
Answer: {2,4,6,8,10}
3) The set B of even numbers between 1 and 10 exclusive.
My answer can only include numbers between 1 and 10. It is NOT okay to include the
endpoints of 1 and 10 because of the word exclusive.
Here are the even numbers between 1 and 10 are: 2,4,6,8,10
10 is an end point and it can’t be part of my answer.
2 is not an end point, so it is okay to put 2 in my answer.
Answer: {2,4,6,8}
5) The set A of solutions to the problem: x + 6 = 10
I need to solve the problem for x:
x + 6 = 10
___-6__-6
x=4
The answer to this is the only number that goes in my set braces.
Answer: {4}
7) The set B of flavors of ice cream in Neapolitan ice cream.
This may take some research if you don’t already know the answer.
Answer: {chocolate, vanilla, strawberry}
Homework #9 – 16. Which of the following sets are well-defined. Write yes for your answer if
the set is well-defined. Write no for your answer if the set is not well-defined.
9) A is the set of goofy dogs.
Answer: NO
not well defined, whether a dog is goofy or not is an opinion and different people may
classify dogs differently.
11) D is the set of numbers whose square is 16.
Answer: Yes
I can create an equation and use Algebra to find the elements of the set. The elements are
4 and -4.
13) The set of years that the Arizona Cardinals won their division.
Answer: Yes
15) The set of cities that have nice climates.
Answer: No
Nice climate is a matter of opinion. Some people will say Phoenix has a nice climate and
others will say it does not. This is the case with most cities.
Homework #17 – 24. Determine whether each set is finite or infinite
17) The set of factors of 12.
The factors of 12 are: 1,2,3,4,6,12
There are only 6 factors of 12.
Answer: Finite
19) The set of multiples of 3.
These are the multiples of 3: {3,6,9,12,15,18…}
It is not possible to list all of the multiples of 3.
Answer: infinite
21) The set of multiples of 4 that are less than 30.
The only multiples of 4 that are less than 30 are
4,8,12,16,20,24,28
It is possible to list them all.
Answer: Finite
23) The set of even natural numbers.
This consists of: {2,4,6,8,10…}
It is impossible to list all of the members of this set.
Answer: Infinite
Homework #25 – 34. Find the cardinal number of the following sets. That is find the number of
elements in each set.
25) The set B of natural numbers between 5 and 10 inclusive.
B contains the elements: 5,6,7,8,9,10
B has 6 elements
Answer: n(B) = 6
27) The set A of even natural numbers greater than 4 and less than 11.
A contains the elements: 6,8,10
A has 3 elements
Answer: n(A) = 3
29) The set A of natural numbers less than 9.
A contains the elements: 1,2,3,4,5,6,7,8
A has 8 elements
Answer: n(A) = 8
31) Find n(A) where A = {1,3,5}
A has 3 elements.
Answer: n(A) = 3
33) Find n(C) where C = {2,4,6,8,10}
C has 5 elements.
Answer: n(C) = 5
Homework #35– 45. Determine whether the sets A and B are equal, equivalent, neither.
35) A = {d,a,b,c} B = {a,b,c,d}
They both have 4 elements, thus they are equivalent.
They have exactly the same elements, thus they are equal.
Answer: equal and equivalent
37) A = {a,b} B = {c,b,a}
They don’t have the same number of elements, thus they are not equivalent.
They don’t have exactly the same elements, thus they are not equal.
Answer: neither
39) A = {0,1,2,3,4} B = {a,b,c,d,e}
They both have 5 elements, thus they are equivalent.
They don’t have exactly the same elements, thus they are not equal.
Answer: equivalent
41) A = {2,1} B = {1,4}
They both have 2 elements, thus they are equivalent.
They don’t have exactly the same elements, thus they are not equal.
Answer: equivalent
43) A = {1} B = {2, 1}
They don’t have the same number of elements, thus they are not equivalent.
They don’t have exactly the same elements, thus they are not equal.
Answer: neither
45) A = {1,3,5,7} B = {7,3,5,1}
They both have 4 elements, thus they are equivalent.
They have exactly the same elements, thus they are equal.
Answer: equal and equivalent