1C sets and venn diagrams

overlapping

"A" and "B" may be overlapping sets meaning that the two sets share some of the same members venn diagram: two overlapping circles

subset

"A" may be a subset of "B" (or vice versa) meaning that all members of "A" are also members of "B" venn diagram: circle "A" inside larger circle "B"

disjoint

"A" may be disjoint from "B" meaning that the two sets have no members in common venn diagram: two circles that do not touch

A company produces work for 250 productions. 175 are​ films, 80 are 3D​ rides, and 25 are motion capture. How many of the productions are purely for 3D​ rides?

80-25 = 55

describe the relationship of the set: democrats & republicans

disjoint, as a person can only be registered for one political party

Choose the first set in the list of natural​ numbers, whole​ numbers, integers, rational​ numbers, and real numbers that describes the following number. 40

natural numbers

the set of natural numbers greater than 5

natural numbers greater than 5: {6, 7, 8, ...} here the dots indicate the list goes on to ever-larger numbers

No S are P

no fish are mammals - S = fish - P = mammals no common members, two separate circles

describe the relationship of the set: nobel prize winners and pulitzer prize winners

overlapping, as a person could win both a pulitzer and nobel peace prize

Consider the sets of natural​ numbers, whole​ numbers, integers, rational​ numbers, and real numbers. Identify from the list above the first set that describes the given number. - 4/3

rational numbers

Some S are P

some doctors are women - S = doctors - P = women overlapping circles for doctors and women, there are some people (at least one) that are both women and doctors

Some S are not P

some teachers are not men - S = teachers - P = men overlapping circles for teachers and men, there are some people (at least one) who are in the teacher's circle but not the men circle (women teachers)

decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). I counted an irrational number of students in my class.

the statement does not make sense. Irrational numbers have​ non-repeating decimal​ expansion, so there could not be an irrational number of students.

An average of many different studies of handedness indicate that in a random sample of ​adults,14 percent of men are​ left-handed and 6 percent of women are​ left-handed. (Assume the rest are​ right-handed.) Suppose you have a sample of 250 women and 100 ​men, in which the numbers of​ left-handed and​ right-handed people reflect the average percentages. Make a​ two-way table that shows the distribution you would find.

women men right handed 235 86 left handed 15 14

the set of years of the cold war, generally taken to have started in 1945 and ended in 1991

years of the cold war {1945, 1946, 1947, ... 1991} here the dots indicate that the list includes all the years between 1947 and 1991 even though they are not listed explicitly

Use set notation to write the members of the following​ set, or state that the set has no members. Odd numbers between 8 and 34 that are multiples of 3.

{9, 15, 21, 27, 33}

the set of countries larger in land area than the united states

{Russia, Canada}

All S are P

all whales are mammals - S = whales - P = mammals whales inside circle of mammals

Consider the set​ {Alabama, Alaska,​ Arizona,..., Wyoming}. What does the​ "..." represent?

It represents the other 46 states of the United States. Because the list is​ alphabetical, there is a basic manner by which the remaining members can be determined.

how can you put a categorical proposition into one of the standard forms if it is not in such a form already?

Rewrite the statement so it has a clear subject set and a clear predicate set.

Use set notation​ (braces) to write the members of the following​ set, or state that the set has no members. The even numbers between and including 50 and 62.

The members of the set are ​{50, 52, 54, 56, 58, 60, 62​}.

Decide whether the following statement makes sense​ (or is clearly​ true) or does not make sense​ (or is clearly​ false). I surveyed my class to find out whether students rode a bike on campus or not. Then I made a Venn diagram with one circle​ (inside a​ rectangle) to summarize the results.

The statement makes sense because students will either answer with ride a bike or not ride a​ bike, which can be summarized using one circle in a Venn diagram.

set: dogs and cats

a pet can be either a cat or dog, not both. draw the venn diagram w/ circles that do not touch, we refer to them as disjoint sets. region inside the rectangle and outside the circles represent pets that aren't cats or dogs (rabbits, birds, reptiles)

What is a​ set? Describe the use of braces for listing the members of a set.

a set is a collection of objects, living or nonliving every member of the set is listed within the​ braces, with each member separated from the next by a comma. If there are too many members to​ list, use three​ dots, ..., to indicate a continuing pattern.

set: whales and mammals

because all whales are mammals , set "whales" is a subset of the set "mammals" draw a circle to represent the set whales inside a circle representing the set mammals the circles are enclosed by a rectangle so there are 3 regions in this diagram: - the circle "whales" represents all whales - region outside the whales circle but inside the mammals circle represents mammals that aren't whales (people, bears, cats) - region outside the mammals circle, inside the rectangle represents non-mammals (birds, fish, insects)

categorical propositions

claim a particular relationship between two categories or sets, must have the structure of a complete sentence. one set appears in the subject of the sentence and the other the predicate ex: " all whales are mammals " - whales are the subject set - mammals are the predicate set " All S are P, where S = whales and P = mammals "

set: nurses and women

considered overlapping sets as it is possible for a woman to be a nurse at the same time and vice versa this venn diagram has four regions since it overlaps - overlap region represents women nurses - nurses circle without overlap region represents male nurses - women circle without overlap represents women who aren't nurses - the region outside both circles (inside rectangle) represents people who are neither nurses or women (men who are not nurses)