Let r and s be binary relations on the set 1 2 3 4 5 where r...

Name: let r and s be binary relations on the set 1 2 3 4 5 where r 1 2 21 34 41 and s 13 24 31 give the ordered pairs of each of the following a 5 points r r b 5 points s r c 5 points r s 46044
Uploaded: 2022-04-17T11:42:34-08:00
Duration: 7 min 53 s
Channel: Shannon K
Description: let r and s be binary relations on the set 1 2 3 4 5 where r 1 2 21 34 41 and s 13 24 31 give the ordered pairs of each of the following a 5 points r r b 5 points s r c 5 points r s 46044

Let 𝑅 and 𝑆 be binary relations on the set {1, 2, 3, 4, 5} where: 𝑅 = {(1, 2), (2,1), (3,4), (4,1)} and 𝑆 = {(1,3), (2,4), (3,1)}. Give the ordered pairs of each of the following. a. [5 points] 𝑅 ∘ 𝑅 b. [5 points] 𝑆 ∘ 𝑅 c. [5 points] 𝑅 ∘ 𝑆

Transcript

00:01 In this question we have given a set that is a is equals to 0 .1, 2, comma 3.

00:09 And we have to affect the given three relations are transitive, reflexive and symmetric or not.

00:17 So for that first we will define what is the meaning of reflexive.

00:27 So, the property says that if a comma a belongs to.

00:35 To the relation r, for every a belongs to a the set, then r is reflexive.

00:50 It means that if for every element in set a we have a order pair of type a comma a in relation r, then the relation is said to be a reflexive relation.

01:03 Now, symmetric.

01:04 It means that if a comma b belongs to r, where a comma b is in a, then b comma a must belongs to r.

01:25 For every a comma b belongs to r.

01:28 Now in transitive, if a comma b belongs to r, b comma c belongs to r, then.

01:42 Then a comma c must belongs to r for every a comma b comma c in a.

01:51 So in order to check each relation we will keep in mind this three definitions.

01:57 So the first relation is given to us is as follows.

02:03 The relation r is set 0 .0, 0 .1, 0 .3, 1 .0 .3 .1.

02:14 1 .0, 1 .1, 2 .2, 3 .0 and 3 .3.

02:25 These are the elements in the set r.

02:28 And we have to check whether the relation r is symmetric, transitive or reflexive.

02:34 Now we'll check for reflexive.

02:41 Here, 0 .0 belongs to r.

02:46 1 .1 is also belongs to r.

02:48 Similarly 2 comma 2 belongs to r and 3 .3 is also belongs to r so it implies r is reflexive now for symmetric we have 0 .1 belongs to r and 1 .0 is also belongs to r similarly, 0 .3 belongs to r and so 3 comma 0 is also belongs to r.

03:32 So this relation is also symmetric...

Question

Let 𝑅 and 𝑆 be binary relations on the set {1, 2, 3, 4, 5} where: 𝑅 = {(1, 2), (2,1), (3,4), (4,1)} and 𝑆 = {(1,3), (2,4), (3,1)}. Give the ordered pairs of each of the following. a. [5 points] 𝑅 ∘ 𝑅 b. [5 points] 𝑆 ∘ 𝑅 c. [5 points] 𝑅 ∘ 𝑆

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