Ole Miss Math 167 exam 1 study terms

Determine the cardinal number of the set. X={1,2,5,8,9,14,15,18}

|X| = 9

Find the number of playing cards in a standard deck of 52 cards that are either spades or black face cards.

16

Find the number of playing cards in a standard deck of 52 cards that are either clubs or black cards without numbers on them.

17

Disjoint

A and B are two sets such that there are no elements in the set A that are also contained in the set B and denoted as A∩B=∅.

equal sets

A and B are two sets that contain exactly the same elements.

Use the given simple statements to write the compound statement b∨a in words. a: It is sunny. b: I am hot.

It is sunny or I am hot.

Negate the following conditional statement. If you are afraid of the dark, I will not turn off the lights.

You are afraid of the dark, and I will turn off the lights.

Negate the following conditional statement. Having the access to the internet is sufficient to get the latest news from all over the world.

You have the access to the internet, and you do not get the latest news from all over the world.

Let A={51,57,58,89,14,47,23}. Which of the following sets is a subset of A?

E={57,47,51,23,14,89}

Which of the following is an example of a mathematical statement? A boyfriend who cheats not a boyfriend at all. I am driving 5 miles an hour over the speed limit. I ate enough for 5 people. 23 is the coolest basketball jersey number.

I am driving 5 miles an hour over the speed limit.

Negate the following conditional statement. I read this book whenever I find it difficult to sleep.

I find it difficult to sleep, and I do not read this book.

Negate the following conditional statement. I listen to this song whenever I miss the ocean.

I miss the ocean, and I do not listen to this song.

Negate the following conditional statement. If John fails this task, his parents will not be happy.

If john fails his task, then his parents will be happy.

Negate the following conditional statement. Entering the correct code is sufficient to get access to the database.

If you enter the correct code, then you DO NOT get access to the database.

Determine the cardinal number of the set. W={t|t∈ℕ, t is even, and |t|<8}

3

Find the number of playing cards in a standard deck of 52 cards that are either kings or black face cards.

8

proper subsets

A and B are two sets such that B is subset of A , and A contains at least one element that is not contained in B

equivalent sets

A and B are two sets that have the same number of elements.

complement

A set that consists of all the elements in the given universal set that are not contained in another setA.

empty set

A set that contains no elements.

roster notation

A way to describe a set by listing all of the elements in the set

Venn Diagram

A way to visualize the relationships between sets which are represented by circles (or ovals) contained within a rectangular region representing the universal set.

If A={s,u,b,t,r,o,p,i,c,a,l} and U ={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z} find A′

A' = {d,e,f,g,h,j,k,m,n,q,v,w,x,y,z}

Use the given sets to find A∩B. A={3,4,5,6,7,8,9,10} B={3,5,7,9,11,13}

A∩B= {3,5,7,9}

Use the given sets to find A∪B. A={2,3,4,5,6,7,8,9} B={3,5,7,9,11,13}

A∪B= {2,3,4,5,6,7,8,9,11,13}

Negate the following conditional statement. Cindy makes stupid jokes whenever she feels uncomfortable.

Cindy feels uncomfortable, and she does not make stupid jokes

Use the variable x to write the set in set-builder notation. Let M be the set of natural numbers less than thirteen.

M= {x|x∈ℕ,x<13}

Use the given sets to answer the question. Is P equal to Q? Why or why not? P={North, East, West, South, Center} Q={x∣x is a cardinal direction}

No, because P has more elements than Q.

Which of the following is the negation for the given statement? Six hundred seventeen girls were inducted on the same day I was inducted.

Six hundred seventeen is not the number of girls who were inducted the same day I was inducted.

universal set

The set of all elements being considered for any particular situation.

Negate the following conditional statement. If you prepare the cake, Andy will not try it.

You prepare the cake, and Andy will try it.

Use the letters given to express the given compound statement in symbolic form. The rocket goes up and it does not come down. a: The rocket goes up. b: The rocket comes down.

a ^ ~b

disjunction

a and b are two statements such that "a or b" is a compound statement which will always be true unless both statements are false.

Identify whether the given statement is conditional or biconditional. My professor is offering extra credit if and only if I attend his office hours.

bicondtional

Which of the following is an example of a mathematical statement? 23 is the coolest jersey number a boyfriend who cheats not a boyfriend at all i am driving 5 miles per hour over the speed limit chocolate milkshakes are delicious

i am driving 5 miles per hour over the speed limit

Use De Morgan's Laws to write an equivalent statement. Sophia has a Bologna dog and she does not have a boston terrier.

it is NOT true that sophia DOES NOT have a bologna dog OR she has a boston terrier.

Use variables to rewrite the given compound statement. Jack has a pet sparrow and Bob does not have a pet. m= Jack has a pet sparrow. n= Bob has a pet.

m ^ ~n

Which of the following is an example of a mathematical statement? nobody drives on highway 16; there is too much traffic 20 is a lucky number jersey chocolate milkshakes are delicious my boyfriend is taller than I am

my boyfriend is taller than I am

ℕ

natural numbers (1,2,3...)

Use the given sets to answer the question. Is P=Q? Why or why not? P={carnation,daisy,rose,lily,daffodil,iris} Q={daisy,lily,orchid,daffodil,iris,peony}

no, because the sets contain different elements

Which of the following is the negation for the given statement? None of the fans are not standing.

not all fans are standing

Use the given sets to find |P∪Q|. U={a,b,c,d,...,x,y,z} P={s,a,m,p,l,e} Q={e,x,c,l,a,i,m}

|P∪Q|= 10