For each case, think of a set S and a binary relation p on S for -
A. p is reflexiveandsymmetric but not transitive
b. p is reflexiveand transitive but not symmetric
c. p is reflexive but neither symmetric nor transitive

Relations
1. Let C = {2, 3, 4, 5} and D = {3, 4} and define a binary relation S from C to D as follows:
for all (x, y) C D, (x, y) S x y.
a) Write S as a set of ordered pairs.
b) Is 2 S 4? Is 4 S 3? Is (4, 4) S? Is (3, 2) S?
2. Let A = {3, 4, 5} and B = {4, 5, 6} and let S be the "divides" rel

Regarding the set of natural numbers N, answer the following questions.
Is â?? a binary relation? Explain.
Is â?? reflexive? Explain.
Is â?? symmetric? Explain.
Is â?? transitive? Explain.
Is â?? an equivalence relation? Explain.

S = {0, 1, 2, 4, 6}
Test the binary relations on S for reflexivity, symmetry ,antisymmetry, and transitivity. Also find the reflexive, symmetricand transitive closure of each relations.
A)
P = {(0,0), (1,1), (2,2), (4,4), (6,6), (0,1), (1,2), (2,4), (4,6) }
B)
P {(0,1), (1,0), (2,4), (4,2), (4,6), (6,4)}
C)
P ((0

Please see the attached file for the fully formatted problems.
SECTION 10.2
For #2: A binary relation is defined on the set A = {0, 1, 2, 3}. For the relation given,
a. draw the directed graph (See drawing tips in the Overview)
b. determine whether the relation is reflexive
c. determine whether the relation is symmetr

Show that the following are equivalent:
(a) ~ is an equivalence relation on a group G
(b) ~ is reflexiveand, for all elements a, b, c of G: if a ~ b and b ~ c, then c ~ a.
See the attached file.

Please help with the following problem regarding discrete math.
I need a clear explanation of what an equivalence relation is with an examples. Specifically given 5|(m-n), where m and n are integers, please verify if this is an equivalence relation.
Please explain this clearly and in detail.

Logic & Set Theory; Boolean Algebra; Relations & Functions
1. How do we distinguish relations from functions?
2. What sort of relation is friendship, using the human or sociological meaning of the word? Is it necessarily reflexive, symmetric, antisymmetric, or transitive? Explain why it is or is not any of these. What othe