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
ElenaW [278]
2 years ago
6

(a) Let R = {(a,b): a² + 3b <= 12, a, b € z+} be a relation defined on z+)

Mathematics
1 answer:
grin007 [14]2 years ago
4 0

Answer:

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Step-by-step explanation:

The relation R is an equivalence if it is reflexive, symmetric and transitive.

The order to options required to show that R is an equivalence relation are;

((a, b), (a, b)) ∈ R since a·b = b·a

Therefore, R is reflexive

If ((a, b), (c, d)) ∈ R then a·d = b·c, which gives c·b = d·a, then ((c, d), (a, b)) ∈ R

Therefore, R is symmetric

If ((c, d), (e, f)) ∈ R, and ((a, b), (c, d)) ∈ R therefore, c·f = d·e, and a·d = b·c

Multiplying gives, a·f·c·d = b·e·c·d, which gives, a·f = b·e, then ((a, b), (e, f)) ∈R

Therefore R is transitive

From the above proofs, the relation R is reflexive, symmetric, and transitive, therefore, R is an equivalent relation.

Reasons:

Prove that the relation R is reflexive

Reflexive property is a property is the property that a number has a value that it posses (it is equal to itself)

The given relation is ((a, b), (c, d)) ∈ R if and only if a·d = b·c

By multiplication property of equality; a·b = b·a

Therefore;

((a, b), (a, b)) ∈ R

The relation, R, is reflexive.

Prove that the relation, R, is symmetric

Given that if ((a, b), (c, d)) ∈ R then we have, a·d = b·c

Therefore, c·b = d·a implies ((c, d), (a, b)) ∈ R

((a, b), (c, d)) and ((c, d), (a, b)) are symmetric.

Therefore, the relation, R, is symmetric.

Prove that R is transitive

Symbolically, transitive property is as follows; If x = y, and y = z, then x = z

From the given relation, ((a, b), (c, d)) ∈ R, then a·d = b·c

Therefore, ((c, d), (e, f)) ∈ R, then c·f = d·e

By multiplication, a·d × c·f = b·c × d·e

a·d·c·f = b·c·d·e

Therefore;

a·f·c·d = b·e·c·d

a·f = b·e

Which gives;

((a, b), (e, f)) ∈ R, therefore, the relation, R, is transitive.

Therefore;

R is an equivalence relation, since R is reflexive, symmetric, and transitive.

Based on a similar question posted online, it is required to rank the given options in the order to show that R is an equivalence relation.

Learn more about equivalent relations here:

brainly.com/question/1503196

You might be interested in
The momentum of an object, p, is determined by its mass, m, and its velocity, v. The formula for this relationship is shown.
timama [110]

Answer:

b

Step-by-step explanation:

7 0
3 years ago
When 2x^2 - 20x + 49 = 19 is written in the form (x - p)^2 = q, what is the value of q? Show your work please.
Strike441 [17]
 = 2x^2 - 20x + 49 = 2(x^2 - 10x + 49/2) 

y= 2((x-5)^2 - 25 + 49/2) = 2((x-5)^2 - 1/2) = 2(x-5)^2 - 1 

q =5, r=-1, p=2 

Vertex = (q,r) = (5,-1)

hope it helps plz mark as brainliest
5 0
3 years ago
Which of the following expression has the greatest value: -3+-4-(-2),-3-(-4)-(-2),-3+-4-2,-3-(-4)-2
AleksAgata [21]
The third one
U solve from left to right and when two negatives are next to each other it turns to a plus.
6 0
2 years ago
If you rolled a fair number cube 1-6, 12 times, about how many times would you expect to roll a 5 or a 6?
Sav [38]
Well it is definately not c haha. I would say 3 because it is a pretty even chance of getting three.
4 0
3 years ago
Factor completely 6x²-4x -2
swat32
6x^2-4x -2 \\ \\ GCF = 2 \\ \\ 2( \frac{6x^2}{2} +  \frac{-4x}{2} -  \frac{2}{2} \ / \ factor \ out \ GCF \\ \\ 2(3x^2 - 2x - 1) \ / \ simplify \ terms \\ \\ 2(3x^2 + x - 3x - 1) \ / \ factor \\ \\ 2(x(3x+1) - (3x + 1)) \ / \ factor \ out \ common \ terms \\ \\ 2(3x+1)(x - 1) \ / \ factor \ out \ common \ term \\ \\ Answer: \fbox {2 (3x + 1)(x - 1)}
7 0
3 years ago
Read 2 more answers
Other questions:
  • Sammy is conducting a science experiment where he has to mix 8.25 ounces of vinegar and 4.30 ounces of lemon juice how many ounc
    13·1 answer
  • Josie has 47$ left on her checking account if she writes a check for 55$ what will josies balance be
    5·1 answer
  • The number of years of education of self-employed individuals in the U.S. has a population mean of 13.6 years and a population s
    11·2 answers
  • 1) 7b – 37 = 4(5b - 6)
    5·2 answers
  • Help plz...............
    14·1 answer
  • Triangle L M Q is cut by perpendicular bisector L N. Angle N L Q is 32 degrees and angle L M N is 58 degrees. Is TriangleMNL ≅ T
    6·2 answers
  • What is a budget? (Need 2 sentences or more)
    14·1 answer
  • Solve: 0 <img src="https://tex.z-dn.net/?f=%5Cleq" id="TexFormula1" title="\leq" alt="\leq" align="absmiddle" class="latex-formu
    6·1 answer
  • Pedro is building a playground in the shape of a right triangle. He wants to know the area of the playground to help him decide
    6·1 answer
  • HELP! DUE AT 5 PM!! 10 BRAINLIST!<br><br> 3x -15x - 30 &gt; 54
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!