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
docker41 [41]
3 years ago
13

Which of these relations on the set {0, 1, 2, 3} are equivalence relations? If not, please give reasons why. (In other words, if

a relation is not an equivalence relation, please list each property that is missing and the reason why it is missing.) (1) {(0,0), (1,1), (2,2), (3,3)} (2) {(0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3)} (3) {(0,0), (1,1), (1,2), (2,1), (2,2), (3,3)} (4) {(0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,2), (3,3)}
Mathematics
1 answer:
Delicious77 [7]3 years ago
5 0

Answer:

(1)Equivalence Relation

(2)Not Transitive, (0,3) is missing

(3)Equivalence Relation

(4)Not symmetric and Not Transitive, (2,1) is not in the set

Step-by-step explanation:

A set is said to be an equivalence relation if it satisfies the following conditions:

  • Reflexivity: If \forall x \in A, x \rightarrow x
  • Symmetry: \forall x,y \in A, $if x \rightarrow y,$ then y \rightarrow x
  • Transitivity: \forall x,y,z \in A, $if x \rightarrow y,$ and y \rightarrow z, $ then x \rightarrow z

(1) {(0,0), (1,1), (2,2), (3,3)}

(3) {(0,0), (1,1), (1,2), (2,1), (2,2), (3,3)}

The relations in 1 and 3 are Reflexive, Symmetric and Transitive. Therefore (1) and (3) are equivalence relation.

(2) {(0,0), (0,2), (2,0), (2,2), (2,3), (3,2), (3,3)}

In (2), (0,2) and (2,3) are in the set but (0,3) is not in the set.

Therefore, It is not transitive.

As a result, the set (2) is not an equivalence relation.

(4) {(0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,2), (3,3)}

(1,2) is in the set but (2,1) is not in the set, therefore it is not symmetric

Also, (2,0) and (0,1) is in the set, but (2,1) is not, rendering the condition for transitivity invalid.

You might be interested in
What is the next three numbers out of the pattern 60 54 48 and 42
aleksandrvk [35]
The next three are 36, 30, and 24
4 0
3 years ago
Five times the sum of m and n in written expression
frozen [14]

Answer:

5(m+n)

Step-by-step explanation:

5 0
3 years ago
For this exponential function what is the output value (y) when the input value (x) is 0?
Alenkinab [10]

Answer:

12

Step-by-step explanation:

y^0=1\\5^0=1\\12*1=12

6 0
3 years ago
Please answer in a little bit detail ​
xeze [42]

Answer:

what the heck i think pre-alegbra is hard what do they expect from us ? the mother freaking world ? like no

Step-by-step explanation:

6 0
3 years ago
Which of these fractions is closest to 0? 2/15 or 4/9 or -4/9
WITCHER [35]

Answer:

2/15

Step-by-step explanation:

If you graph it on a line, 2/15 will be the closest to 0.

5 0
2 years ago
Read 2 more answers
Other questions:
  • Rachel is baking a cake but does not know if she wants to bake a round or a square cake. which cake has a larger area a round 8
    8·1 answer
  • one number is 4 times a first number. A third number is 100 more than the first number. if the sum of the three numbers is 592 f
    9·1 answer
  • What is the cosine of 45°
    10·1 answer
  • Can someone help me pls on this question
    11·1 answer
  • Can someone solve this?
    14·1 answer
  • Evaluate |x^2 +9x| at x = -4
    13·1 answer
  • HELP ME PLSSSSSS IM ALMOST DONE !!! Owen took a road trip to Utah. He traveled 615 miles. He put a total of 30 gallons of gas in
    5·1 answer
  • Anyone willing to do my math class on edg?
    10·2 answers
  • What is the equation of the midline?
    6·1 answer
  • Please Help Me With This Please!​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!