Question

Determine whether the given relation is an equivalence relation on {1,2,3,4,5}. If the relation is an equivalence relation, list the equivalence classes (x, y E {1, 2, 3, 4, 5}.)

{(1,1), (2,2), (3,3), (4,4), (5,5), (1,3), (3,1), (3,4), (4,3)}

If the relation above is not an equivalence relation, state that the relation is not an equivalence relation and why.

Example: "Not an equivalence relation. Relation is not symmetric"

Remember to test all pairs in relation R

Answer #1

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Consider the relation R= {(1,2),(2,2),(2,3),(3,1),(3,3)}. Is R
transitive, not reflexive, symmetric or equivalence relation?

Show that the relation
R={(1,1),(1,4),(2,2),(2,3),(3,3),(3,2),(4,1),(4,4)} is an
equivalence relation and contrust the associated directed
graph.

Question 1: Roll two fair dice. Then the sample space S is the
following.
S =
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Let E be the event that the sum of the dice is odd, let F be the
event that the first die lands on 1,
and let G...

1. Two dice are rolled. There are 36 possible outcomes, the
sample space is:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4)
(2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3)
(4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2)
(6,3) (6,4) (6,5) (6,6)
A = ‘second roll is a 6’
B = ‘sum of two dice equals 7’
C = ‘sum of two dice equals 3’
a. What is P(B|A)?
b. What is...

2. Consider a ten-sided die of which the sides display the
numbers 1, 2, 3, and 4 according to this table:
side of die 1 2 3 4 5 6 7 8 9 10 number displayed 1 1 1 1 2 2 2 3 3
4
Rolling two such dice is an experiment with the sample space S =
(1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4) (3,1)
(3,2) (3,3) (3,4) (4,1) (4,2) (4,3)...

9K)Below is a list of all possible outcomes in the experiment of
rolling two die. (If the grid pops up twice, pay attention to only
one table. Having formatting issues, apologies! And thank you for
your help!
1,1
1,2
1,3
1,4
1,5
1,6
2,1
2,2
2,3
2,4
2,5
2,6
3,1
3,2
3,3
3,4
3,5
3,6
4,1
4,2
4,3
4,4
4,5
4,6
5,1
5,2
5,3
5,4
5,5
5,6
6,1
6,2
6,3
6,4
6,5
6,6
Determine the following probabilities. Write your answers...

Determine whether the given statement is true or false. Explain
your answer.
(a) If R is an antisymmetric relation, then R is not
symmetric.
(b) If John Jay College was founded in 1997, then the moon is
made of cheese. (
c) ∀x∃y(x divides y) where the domain of discourse for both
variables is {2, 3, 4, 5, 6}.
(d) ∃x∀y(x divides y) where the domain of discourse for both
variables is {2, 3, 4, 5, 6}.
(e) ∀n(3n ≤...

Relations and Functions
Usual symbols for the above are;
Relations: R1, R2, S, T, etc
Functions: f, g, h, etc. But remember a function is a special
kind of relation so it might turn out that a Relation, R, is a
function, too.
Relations
To understand the symbolism better, let’s say the domain of a
relation, R, is A = { a, b , c} and the Codomain is B = {
1,2,3,4}.
Here is the relation: a R 1, ...

1. Write the following sets in list form. (For example, {x | x
∈N,1 ≤ x < 6} would be {1,2,3,4,5}.) (a) {a | a ∈Z,a2 ≤ 1}. (b)
{b2 | b ∈Z,−2 ≤ b ≤ 2} (c) {c | c2 −4c−5 = 0}. (d) {d | d ∈R,d2
< 0}.
2. Let S be the set {1,2,{1,3},{2}}. Answer true or false: (a) 1
∈ S. (b) {2}⊆ S. (c) 3 ∈ S. (d) {1,3}∈ S. (e) {1,2}∈ S (f)...

using mysql lyrics.database. i will provide the lyrics schema
database info below
1. List the first name, last name, and region of members who do
not have an email.
2. List the first name, last name, and region of members who do
not have an email and they either have a homephone ending with a 2
or a 3.
3. List the number of track titles that begin with the letter
's' and the average length of these tracks in...

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