business math test 1

Determine the cardinal number of the set. X={a∣a∈ℤ, a is even, and |a|≤10}

|X|=11

Write the set using the roster method. K={x∣47≤x<56 and x is not a multiple of 3}

K={47,49,50,52,53,55}

Use the given sets to answer the question. Is P=Q? Why or why not? P={spinach,celery,tomato,onion,carrot} Q={carrot,celery,onion,spinach,tomato}

Yes, because both sets contain exactly the same elements, just in a different order.

Use the given sets to answer the question. Is P equivalent to Q? Why or why not? P={red, orange, yellow, green, cyan, blue, violet} Q={x∣x is a day of the week}

Yes, because both sets contain the same number of elements.

Negate the following conditional statement. Entering the last four digits of your phone number is sufficient to get into the system.

You enter the last four digits of your phone number, and you do not get into the system.

Choose the term that best matches the given definition. 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=∅.

Disjoint

Choose the term that is defined in the given statement. A set that contains no elements.

Empty Set

Choose the term that is defined in the given statement. A and B are two sets that have the same number of elements.

Equivalent Sets

Which of the following is an example of a mathematical statement? I am driving 55 miles an hour over the speed limit. I ate enough for 5 people 20 is a lucky jersey number A boyfriend who cheats not a boyfriend at all

I am driving 55 miles an hour over the speed limit.

Negate the following conditional statement. I visit Angela whenever I come to England.

I come to England, and I do not visit Angela.

Negate the following conditional statement. I get nervous whenever I enter the classroom.

I enter the classroom, and I do not get nervous.

Negate the following conditional statement. If I feel cold, I will not open the window.

I feel cold, and I will open the window.

Use the given simple statements to write the compound statement a∨b in words. a: I like apples. b: I like oranges.

I like apples or I like oranges.

Negate the following conditional statement. If I wake up late, I will not be on time.

I wake up late, and I will be on time.

Use De Morgan's Laws to write an equivalent statement. I am going to study pharmacology and I am not going to study zoology.

It is not true that I am not going to study pharmacology or I am going to study zoology.

Use De Morgan's Laws to write an equivalent statement. During our trip we visited Brazil and we did not visit Argentina.

It is not true that during our trip we did not visit Brazil or we visited Argentina.

Write the set using the roster method. A is the set of positive three-digit numbers where the first digit is smaller than the second by 4 and the third digit is smaller than the first by 2

A={260,371,482,593}

Which of the following is the negation for the given statement? None of the sandwiches are not delicious.

At least one of the sandwiches is not delicious.

Use the given sets to find A∩(B∪C). U={a,b,c,d,...,x,y,z} A={a,l,t,e,r} B={c,r,i,m,e} C={t,h,i,m,b,l,e}

A∩(B∪C)={l,t,e,r}

Use the given sets to find A∩B. A={2,3,4,5,6,7,8,9,10,11} B={3,5,7,9,11,13}

A∩B={3,5,7,9,11}

Use the given sets to find A∪B. A={4,5,6,7,8,9,10,11,12,13} B={3,5,7,9,11,13}

A∪B={3,4,5,6,7,8,9,10,11,12,13}

Identify whether the given statement is conditional or biconditional. I have coffee if and only if I stay up late.

Biconditional Statement

Which of the following is the negation for the given statement? None of the girls are not dancing.

Not all of the girls are dancing.

Choose the term that is defined in the given statement. 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.

Proper Subset

Choose the term that is defined in the given statement. A way to describe a set when all the members of the set share certain properties.

Set-Builder Notation

Choose the term that is defined in the given statement. A table that has a row for each possible combination of truth values of the individual statements that make up the compound statement.

Truth Table

Use variables to rewrite the given compound statement. We will go fishing or we will go swimming.

a: We will go fishing. b: We will go swimming. Statement: a∨b

=> meaning

conditional: "if, then"; always be true unless statement p is true and statement q is false

⋀ meaning

conjunction: "and"; true only when only when both statements are true

⋁ meaning

disjunction: "or"; true as long as at least one of the statements is true

∩

intersection: set that contains all elements common to both sets A and B (only includes the alike elements)

a statement that is true in all possible circumstances

tautology

u meaning

union: set that contains all elements in set A or set B (combines the elements)

Use the given sets to find |A∪B|. U={a,b,c,d,...,x,y,z} A={z,e,p,h,y,r} B={c,r,a,z,y}

|A∪B|=8

Determine the cardinal number of the set. W={m,x,q,f,k,b,s,w,r,e,j,c}

|W|=12

If A={d,r,e,n,c,h} 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′∣=20

Use the letters given to express the given compound statement in symbolic form. If the water is not cold, then you cannot wear a wetsuit. a: The water is cold. b: You can wear a wetsuit.

∼a⇒∼b