PYTHON---Please help 1. See the following relations : R, S, T, , and A × A : R =
ID: 3777291 • Letter: P
Question
PYTHON---Please help
1. See the following relations :
R, S, T, , and A × A : R = {(1, 1), (1, 2), (1, 3), (3, 3)} S = {(1, 1)(1, 2), (2, 1)(2, 2), (3, 3)} T = {(1, 1), (1, 2), (2, 2), (2, 3)}
= empty
relation A × A = universal relation
Select the SINGLE statement which BEST describes above relations :
R,S, , and A × A are all symmetric
Both R and S are symmetrical, while S, , and A × A are symmetric.
R is not reflexive or transitive, while S, , and A × A are symmetric.
R is reflexive, but not transitive, while S and A × A are reflexive
2.
Consider the following 5 relations:
(1) Relation (less than or equal) on the set Z of integers.
(2) Set inclusion on a collection C of sets.
(3) Relation (perpendicular) on the set L of lines in the plane.
(4) Relation || (parallel) on the set L of lines in the plane.
(5) Relation | of divisibility on the set N of positive integers. (Recall x | y if there exists z such that xz = y.)
Choose the BEST, SINGLE answer which describes a TRUE statement:
a. 1, 3, and 4 is reflexive.
b. 1, 2 ,and 5 are reflexive.
c. Only 1 and 2 are reflexive.
d. None are reflexive.
3.
Consider the following 5 relations:
(1) Relation (less than or equal) on the set Z of integers.
(2) Set inclusion on a collection C of sets.
(3) Relation (perpendicular) on the set L of lines in the plane.
(4) Relation || (parallel) on the set L of lines in the plane.
(5) Relation | of divisibility on the set N of positive integers. (Recall x | y if there exists z such that xz = y.)
Choose the BEST, SINGLE answer which describes a TRUE statement:
a. 1 and 2 are symmetric, but 3 is not symmetric
b. 3,4,and 5 are symmetric
c. 1, 3 and 4 are symmetric
d. 3 and 4 are symmetric
4. Each student in Liberal Arts at some college has a mathematics requirement A and a science requirementB.
A poll of 140 sophomore students shows that:
60 completed A, 45 completed B, 20 completed both A and B.
Select the single, TRUE statement the describes (a), (b), and (c):
(a) At least one of A and B;
(b) exactly one of A or B;
(c) neither A nor B.
n(A) = 60
n(B) = 45
n(A B) = 20
n(U) = 140
All of the above
5. Select the single, best answer.
Consider functions mentioned in line (a) and (b).
Select the single answer which BEST describes the following functions is one-to-one? Which is onto?
a. f : N N f (m) = m + 2
b. g : Z Z g(m) = 2m2 7
a.
Function "a" is 'one to one' and 'unto.'
b.
Function "a" is 'one to one.'
c.
Function "b" is 'one to one.'
d.
Function "b" is 'one to one' and 'unto.'
6. Find the following cardinalities:
A={a, b, c, ... ,y, z},
B={x|xN, x2 =5}
7. Is the relation ‘x=y’ reflexive, symmetrical, and/or transitive? Explain which ones they are and why or why not?
Is the relation ‘x != y’ reflexive, symmetrical, and/or transitive? Explain which ones they are and why or why not?
R,S, , and A × A are all symmetric
Explanation / Answer
1. Relation "R" is not reflexive because, it won't have the following element (2,2).
Relation "R" is not symmetric because, it won't have (2,1) and (3,1)
Relation "R" is not transitive
For relation R to be relfexive and symmetric, then R should possess the following
(2,2),(2,1) and (3,1) in addition to the given elements
Relation "S" is Reflexive, because it has (1,1),(2,2),(3,3)
Relation "S" is symmetric, because it has (1,2) and (2,1)
Relation "S" is transitive
And Phi and AXA are always satisfies all the properties of relations.
Hence The answer for you question is option "b".
2. <= is reflexive, because every element in Z satisfies it.
Ex: 1<=1, -4<=-4
Set inclusion is reflexive because each element is subset of itself
Perpendicular relation is not reflexive because, if each line is parallel to itself but not perpendicular.
Parallel relation is reflexive because each line is parallel to itself. Hence reflexive
| relation is reflexive because every number can divide itself.
hence from your options, 'b' is the correct answer.
3. <= is not symmetric because 1<=2 but not 2<=1
Set inclusion is also not symmetric because if A is subset of B, then it doesn't mean that B must be subset of A
Perpendicular relation is symmetric because, if A is perpendicular to B, then it implies that B is also perpendicular to A
|| relation is also symmetric.
| relation is not symmetric because , for exampe 2 divides 4 but not 4|2.
Hence from the options "d" is the correct answer
4. since 20 students completed both, hence A^B=20, then,
the number of students did only requirements A is 60=20=40
the number of students did only requirement B is 45-20=25
The following are the answers to options a,b,c
(a) atleast one of A and B means either A did or B did or both = 40+25+20=85
(b) exactly one of A or B = 40+25=65
(c) neither A nor B = 140-85=55
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