Write the set containing two females in terms of A and B. e. List the elements in !A, AB, AuB (union), and !(AB).
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
Five applicants (Jim, Don, Mary, Sue, and Nancy) are available for two identical jobs. A supervisor selects two applicants to fill these jobs.
a. List all possible ways in which the jobs can be filled. (That is, list all possible selections of two applicants from the five.)
ans: S = {JD, JM, JS, JN, DM, DS, DN , MS, MN, SN}
b. Let A denote the set of selections containing at least one male. How many elements are in A?
ans : A = {JM, JS, JN, DM, DS, DN, JD}
Set A contains 7 elements
c. Let B denote the set of selections containing exactly one male, How many elements are in B?
ans : A = {JM, JS, JN, DM, DS, DN}
Set A contains 6 elements
d. Write the set containing two females in terms of A and B.
e. List the elements in !A, AB, AuB (union), and !(AB).
Note: I need help with parts d and e.
According to the given information,
Where the set '' represents all the possible ways of selecting two applicants out of two male and three female applicants, the set '' represents the possible ways of selecting two applicants such that at least one of them is a male applicant, and the set '' represents the possible ways of selecting two applicants such that exactly one of the two selected applicant is male.
- Union of two set: is the union of two sets and , which contains all elements of set and set , without any repetition of any element.
- Intersection of two sets: is intersection of two set and , which contains all the elements present in both sets and .
- Complement of set: is complement of set , containing all those elements of universal set which are not present in .
- Universal Set: Universal set is a set which has all the elements of all related sets, without the repetition of any element.
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