7.1 basic set concepts : finite math 110 quiz

A symbol that looks like E means ( € )

"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.

Looking at R = {8, 4, 9, 1} we see that 0 is not listed among the elements of R

0 € R (The E symbol should have a dash through it)

5 € {5, 7, 10}

5 is an element of the set

The number of subsets of a set A can be found using the formula number of subsets of

A = 2n(4) where n(A) is the number of distinct elements in the set.

A n B

A intersect B What they have in common

Two sets are called disjoint if

A n B = 0 with a dash through it

(A U B) stands for

A union B, which includes any elements in A or in B, or in both

Given the sets S = {a, b, c, d} and T = {1,2, 3}, the union S U T is the set which includes all elements that are either in S or in T, or both (ignoring duplicates).

Because all of the elements (members) of these sets are distinct, the union of these two sets is given by effectively combining the sets into one large set. So, we have S U T = {a, b, c, d, 1, 2, 3}

The items in a collection are called a ______

Element

S = {states that start with the letter B}

Has no elements, since no states starts with B

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.

Here 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 Each set has exactly one empty subset. Thus the total number of non-empty subsets for A is 128 - 1 = 127.

To find the elements of A U B, we take all of the elements of each set and dump them into a single set, so to speak, while ignoring any repeated elements.

Here, A U B = {0, 2, 3, 4, 7, 8}. Remember the order in sets does not matter, so while A U B does have a natural order to its elements, they can be given in any order.

To find the elements of A n B, we look for which elements are common to both set A and set B.

In this case, both A and B have elements 0, 7, and 8, and thus An B = {0, 7, 8}.

Tall people 6 foot or taller

Is a set

Good tv shows

Is not a set because it is subjective

For the next option, is 1 € Q?

Looking at the list of elements of Q we see 1 is in that list, and so it is true that 1 € Q.

(A U B) ^ 1

Means everything that's in the universal set that's not in set A or B

Tall people is

Not a set

The union S U T is the

Set which includes all elements that are either in S or in T, or both (ignoring duplicates)

Now we need to calculate (A U B) ^ C. What is A U B? What elements are in U and are NOT in A U B?

The notation A U B means "A union B", which includes any element in A or in B, or in both. So A U B = {a, b, d, e, 1, 2, 3}, and then the only element of U that's left out is c. So (A U B) ^ C = {c}.

If it is specific

Then yes it is a set

Some sets are finite, and some sets are infinite.

There are also sets which have zero elements.

To compute (BUC) n A, we will first take the union of B and C, then intersect that resulting set with A. We see that BUC = {1, 2, 4, 5, 6, 7, 9, 10}. This set only has the elements 1, 4, and 9 in common with the set A = {1, 3, 4, 8, 9}.

Thus, we conclude that (BUC) n A = {1,4, 9}.

A U B

Union of A and B (all the data contained in set A or B or both). Everything in each set

The union of two sets is the collection of all elements that appear in either set (and we typically don't write duplicates if they appear). ( the symbol looks like a U )

We conclude that A U B = {1, 2, 3, 4, 5, 7, 8, 9}. All of these numbers appear in at least one of the two sets, A or B.

A = {1,3,4,8,9} and B = {2, 5, 7} don't have any elements in common, so their intersection is the empty set, typically denoted 0 with a dash through it.

We write: A n B = 0. (The 0 should have a dash through it)

A set is

a well-defined collection of objects, in which it is possible to determine if a given object is in the collection.

B' is the complement of the set B

and will contain all the elements of the universal set U that are not in the set B.

The intersection of two sets is the ( symbol that looks like an n )

collection of all elements that both sets have in common.

R = {18, 4, 9, 1} True or false

contains the elements 1 and 4, it does not contain the set {1, 4} so this one is not true.

A set of n distinct elements

has 2 ^ n total subsets.

Remember that "n" means

intersection

The union of two sets A U B

is the collection of all of the elements from each set thrown together into one big set.

Finally the intersection A n B of two sets

is the collection of elements that is common to both sets -- their overlap.

A^c (A complement)

means the set of elements in the universal set that are NOT in A.

A = {6, 7, 10, 15, 19}

n (5) , and so number of sets is 2 ^ 5 = 35 2 x 2 x 2 x 2 x 2 = 35

C = 0 with a dash through it

n (c) = 0 , then C has 2 ^ 0 = 1 subset

order of operations for sets:

parenthesis, complements, and then unions / intersections from left to right. So to find the elements of A n B', we first start with B', and then find the overlap with A.

We use the symbol € with a dash over it

to say an item is not an element of

In this case, since A = { red, cyan, teal, olive, blue}, we have that n (A) = 5. Using the formula above,

we get the number of subsets of A is 2n(A) = 2^5 (2x2x2x2x2) = 32.