1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
TEA [102]
3 years ago
11

Determine which of the following are equivalence relations and/or partial ordering relations for the given sets: A = { lines in

the plane } , and r defined by x r y if and only if x is parallel to y . Assume every line is parallel to itself. A = R and r defined by x r y if and only if | x − y | ≤ 7
Mathematics
1 answer:
VLD [36.1K]3 years ago
8 0

Answer:

Check the explanation

Step-by-step explanation:

1

a) A is an Equivalence Relation

Reflexive : x is parallel to itself => x R x

Symmetric : x is parallel to y => y is parallel to x.

Therefore x R y => y R x

Transitive :  x is parallel to y and y is parallel to z then x, y, z are parallel to each other.

=> x R y and y R z => x R z

Therefore A is equivalent.

1. b)

x r y if and only if |x-y| less than or equal to 7

Reflexive : |x-x| = 0 <= 7 => x R x Satisfied.

Symmetric : let x R y => |x-y| <= 7

Consider |y-x| = |(-1)*(x-y)| = |x-y| <= 7

=> y R x => Satisfied

Transitive : let x R y and y R x

=> |x-y| <= 7 and |y-z| <= 7

but this doesn't imply x R z

Counter-Example : x = 1, y = 7, z = 10

Therefore this relation is neither Equivalent nor Partial Order Relation.

You might be interested in
The sum of two number is 14 and their difference is 10 then what will be their multiplication
Tomtit [17]

12+2=14

12-2=10

12 x 2= 24

3 0
3 years ago
If there are 400 ounces in 25 pounds, how many ounces are in 8 pounds
ladessa [460]
The answer is:  " 128 oz. " . 
_________________________________________________________
There are:  " 128 oz. " (in " 8 lbs." ) .
_________________________________________________________
Explanation:
________________________________________________________
Set up a proportion;  as a fraction; as follows:
________________________________________________________

 400/ 25  = x / 8 ; 

in which:  "x" = the number of "ounces [oz.] there are in "8 lbs." ;
________________________________________________________
We shall solve for "x" , the answer to the problem:

Cross-factor multiply:

25x = (400) * 8 ; 

→ 25x = 3200 ; 

Divide each side of the equation by "25" ; to isolate "x" on one side of the equation; & to solve for "x" ; 

→ 25x / 25 = 3200 / 25 ; 

→  x = 128 .
_________________________________________________________
Answer:  " 128 oz. " . 
_________________________________________________________
There are:  " 128 oz. " (in " 8 lbs." ) .
_________________________________________________________

Note of interest:  " 16 oz. =  1 lb. " (exact conversion). 

So;  "8 lbs.  <span>=  ?</span>  oz. " ; 

→  " 8 lbs. * (16 oz/ 1 lb)  =   ( 8 * 16) oz.  =  128 oz. ;  →  which is our answer!
_________________________________________________________
3 0
2 years ago
Read 2 more answers
Need help on answering 20.
Reptile [31]
N=64.
32+64=100
64/8=8
sqrt (64+225)= sqrt (289) = positive and negative 17
8 0
2 years ago
What is the e at the end of a scientific number?
kherson [118]
Scientific notation is another way to write a number. In scientific notation, the letter E is used to mean "10 to the power of." For example, 1.314E+1 means 1.314 * 101 which is 13.14 .
6 0
3 years ago
after selling tickets to a dance for $3.25 each, the student council brought in $1020.50from tocket sales. how many tickets did
balu736 [363]

3.25x = 1020.50

/3.25     /3.25

x = 314 tickets sold.

7 0
3 years ago
Other questions:
  • Over the summer, Jackie played video games 3 hours per day. When school began in the fall, she only allowed to play video games
    12·1 answer
  • What is the answer to number 12
    9·1 answer
  • If A = James's present age, write an expression for his age seven years from now.
    10·1 answer
  • How to find out how many number combinations if numbers cannot repeat?
    7·1 answer
  • An airplane do you sans 1.5 miles to an elevation of 5.25 miles. Find the elevation of the plane before it’s descent.
    12·1 answer
  • Find the value of n<br><br>Can you guys help me??
    8·2 answers
  • 1. What represents the independent or x variable?
    8·1 answer
  • What is the equation of this line?<br><br> y=3x−2<br><br> y=13x−2<br><br> y=2x−3<br><br> y=12x−3
    15·1 answer
  • How should the decimal point in 0.937 change to get the correct answer to 0.937 ÷ 10²?
    13·2 answers
  • An example of an ordered pair is (1, 5). True or False
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!