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
Sidana [21]
3 years ago
6

Check whether the relation R on the set S = {1, 2, 3} is an equivalent

Mathematics
1 answer:
kozerog [31]3 years ago
3 0

Answer:

R isn't an equivalence relation. It is reflexive but neither symmetric nor transitive.

Step-by-step explanation:

Let S denote a set of elements. S \times S would denote the set of all ordered pairs of elements of S\!.

For example, with S = \lbrace 1,\, 2,\, 3 \rbrace, (3,\, 2) and (2,\, 3) are both members of S \times S. However, (3,\, 2) \ne (2,\, 3) because the pairs are ordered.

A relation R on S\! is a subset of S \times S. For any two elementsa,\, b \in S, a \sim b if and only if the ordered pair (a,\, b) is in R\!.

 

A relation R on set S is an equivalence relation if it satisfies the following:

  • Reflexivity: for any a \in S, the relation R needs to ensure that a \sim a (that is: (a,\, a) \in R.)
  • Symmetry: for any a,\, b \in S, a \sim b if and only if b \sim a. In other words, either both (a,\, b) and (b,\, a) are in R, or neither is in R\!.
  • Transitivity: for any a,\, b,\, c \in S, if a \sim b and b \sim c, then a \sim c. In other words, if (a,\, b) and (b,\, c) are both in R, then (a,\, c) also needs to be in R\!.

The relation R (on S = \lbrace 1,\, 2,\, 3 \rbrace) in this question is indeed reflexive. (1,\, 1), (2,\, 2), and (3,\, 3) (one pair for each element of S) are all elements of R\!.

R isn't symmetric. (2,\, 3) \in R but (3,\, 2) \not \in R (the pairs in \! R are all ordered.) In other words, 3 isn't equivalent to 2 under R\! even though 2 \sim 3.

Neither is R transitive. (3,\, 1) \in R and (1,\, 2) \in R. However, (3,\, 2) \not \in R. In other words, under relation R\!, 3 \sim 1 and 1 \sim 2 does not imply 3 \sim 2.

You might be interested in
What is the 6th term of the geometric sequence shown?
solniwko [45]

Answer:

0

Step-by-step explanation:

subtract 20 from 40 it's Zero

8 0
3 years ago
What is the surface area of this triangular prism? The base of each triangle is 42 m and the height of the triangular base is 20
shutvik [7]

<u>Given</u>:

The base of each triangular base is 42 m.

The height of each triangular base is 20 m.

The sides of the triangle are 29 m each.

The height of the triangular prism is 16 m.

We need to determine the surface area of the triangular prism.

<u>Surface area of the triangular prism:</u>

The surface area of the triangular prism can be determined using the formula,

SA=bh+(s_1+s_2+s_3)H

where b is the base of the triangle,

h is the height of the triangle,

s₁, s₂ and s₃ are sides of the triangle and

H is the height of the prism.

Substituting the values, we get;

SA=(42)(20)+(42+29+29)(16)

SA=840+(100)(16)

SA=840+1600

SA=2440

Thus, the surface area of the triangular prism is 2440 m²

8 0
3 years ago
Giving the brainliest answer to who can ever help me out!!! need help asap!
V125BC [204]

Answer: I think the answer is B

Step-by-step explanation:

7 0
3 years ago
{[20/(8+2)]^6+6}/(4^2/2)
Naddika [18.5K]
So for this problem we need to do order of operations so the very first step that we need to do here is (8+2) because that is the smallest enclosed symbols (8+2)=10 next divide by 20 because that is the next step in the equation which 20/10=2, so now we have {[2]^6+6} and due to order of operations the next step here is to take 2 to the power of 6 which is 64 so now we have {64+6} which is 70 so now we have 70/(4^2/2) and due to order of operations we do the parentheses first and that would mean that we do 4^2 because exponents come after parantheses like so,
70/(16/2) now we do 16/2 because its still inside the paranthesess so 16/2=8 so now we have 70/8 and that equals are end answer of 8.75 Enjoy!=)
7 0
3 years ago
Read 2 more answers
How can you use order numbers that are written as fractions, decimals, and percents?
galina1969 [7]
2.5 4/5 8% that is an example of written fractions decimal and percents
7 0
3 years ago
Other questions:
  • A ball is dropped from a height of 36 feet. At each bounce the ball reaches a height that is three quarters of the previous heig
    13·2 answers
  • which word equation is used to calculate the acceleration of an object. A)add the initial velocity and final velocity and multip
    15·1 answer
  • Tan A tan (60° +A) tan (60° - A)= tan 3A​
    7·1 answer
  • Which of the following expressions is correct?
    15·2 answers
  • Write an inequality for the following: Joe has $53. He needs at least $76 to buy the jacket he wants. How much more money does h
    8·1 answer
  • What are the best tips for studying your exam
    12·2 answers
  • Helpppppppppppppppppppppp
    12·2 answers
  • PLEASE HELP ASAP!!!!Write the ratio as a fraction in lowest terms. 9 pounds to 36 pounds.(50 points!!)
    6·2 answers
  • Please help me with this :)
    5·1 answer
  • What is the area of the triangle formed from (0,-3), (0,4), and (4,-3)?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!