7.1 BASIC SET CONCEPTS : FINITE
MATH 110 QUIZ EXAM 100% SOLVED
2025
A symbol that looks like E means
( € ) - ANSWERS"element of"
and is true if the element on the left shows up, exactly as is, in the list of elements in the
set on the right.
R = {18, 4, 9, 1}
True or false - ANSWERScontains the elements 1 and 4, it does not contain the set {1,
4} so this one is not true.
For the next option, is 1 € Q? - ANSWERSLooking at the list of elements of Q we see 1
is in that list, and so it is true that 1 € Q.
Looking at R = {8, 4, 9, 1} we see that 0 is not listed among the elements of R -
ANSWERS0 € R
(The E symbol should have a dash through it)
The number of subsets of a set A can be found using the formula
number of subsets of - ANSWERSA = 2n(4)
where n(A) is the number of distinct elements in the set.
In this case, since A = { red, cyan, teal, olive, blue}, we have that n (A) = 5.
Using the formula above, - ANSWERSwe get the number of subsets of A is 2n(A) = 2^5
(2x2x2x2x2) = 32.
Let A = {1, 3, 4, 5, 7,9,10}. How many proper subsets does the set have?
Recall that the number of subsets that a set has is defined to be 2(A), where n(A) is the
number
of distinct elements in A. - ANSWERSHere A has 7 elements, so n(A) = 7.
Step 2
Thus according to the formula, the set A has 27 = 128 total subsets. However, this
question
asks for the total number of non-empty subsets, so we need to take out any of these
subsets that are empty. How many of those are there?
Step 3
MATH 110 QUIZ EXAM 100% SOLVED
2025
A symbol that looks like E means
( € ) - ANSWERS"element of"
and is true if the element on the left shows up, exactly as is, in the list of elements in the
set on the right.
R = {18, 4, 9, 1}
True or false - ANSWERScontains the elements 1 and 4, it does not contain the set {1,
4} so this one is not true.
For the next option, is 1 € Q? - ANSWERSLooking at the list of elements of Q we see 1
is in that list, and so it is true that 1 € Q.
Looking at R = {8, 4, 9, 1} we see that 0 is not listed among the elements of R -
ANSWERS0 € R
(The E symbol should have a dash through it)
The number of subsets of a set A can be found using the formula
number of subsets of - ANSWERSA = 2n(4)
where n(A) is the number of distinct elements in the set.
In this case, since A = { red, cyan, teal, olive, blue}, we have that n (A) = 5.
Using the formula above, - ANSWERSwe get the number of subsets of A is 2n(A) = 2^5
(2x2x2x2x2) = 32.
Let A = {1, 3, 4, 5, 7,9,10}. How many proper subsets does the set have?
Recall that the number of subsets that a set has is defined to be 2(A), where n(A) is the
number
of distinct elements in A. - ANSWERSHere A has 7 elements, so n(A) = 7.
Step 2
Thus according to the formula, the set A has 27 = 128 total subsets. However, this
question
asks for the total number of non-empty subsets, so we need to take out any of these
subsets that are empty. How many of those are there?
Step 3
