Let X be the set {1, 2, 3}.
a)For each function f in the set of...
Let X be the set {1, 2, 3}.
a)For each function f in the set of functions from X to X,
consider the relation that is the symmetric closure of the function
f'. Let us call the set of these symmetric closures Y. List at
least two elements of Y.
b) Suppose R is some partial order on X. What is the smallest
possible cardinality R could have? What is the largest?
Let S = {0,1,2,3,4,5,6,7,8}. Test the following binary relation
on S for reflexivity, symmetry, antisymmetry, and...
Let S = {0,1,2,3,4,5,6,7,8}. Test the following binary relation
on S for reflexivity, symmetry, antisymmetry, and transitivity. xρy
if and only if x+y = 8.
Is ρ an equivalence relation?
If we change the relation to x ρ y if and only if x+y 6 8 how
will the cardinality of ρ change? Give a detailed explanation.
2. draw the Hasse
diagram for the partial ordering “x divides y” on the set
{24,3,4,12,96,15,21,36}. Name any least elements, minimal elements,
greatest...
1. Consider the following situation: The universal set U
is given by: U = {?|? ?...
1. Consider the following situation: The universal set U
is given by: U = {?|? ? ? , ? ≤ 12}
A is a proper subset of U, with those numbers that are
divisible by 4.
B is a proper subset of U, with those numbers that are
divisible by 3.
C is a proper subset of U, with those numbers that are
divisible by 2
a) Using Roster Notation, list the elements of sets U, A, B and
C....
a. What are the maximal and minimal elements, if any, of the
set (N+,|)? Is there...
a. What are the maximal and minimal elements, if any, of the
set (N+,|)? Is there a minimum or maximum element?
(N+={1,2,3,4,...}).
b. There are five flavors of icecream: banana, chocolate,
lemon, strawberry and vanilla. We can have three scoops. How many
variations will there be?
Using only the periodic table, arrange each set of atoms in
order of decreasing radius.
Part...
Using only the periodic table, arrange each set of atoms in
order of decreasing radius.
Part A
Rank elements from largest atomic radius to smallest
atomic radius.
Na, Ra, and Sr:
Part B
Rank elements from largest atomic radius to smallest
atomic radius.
As, In, and Sn:
Part C
Rank elements from largest atomic radius to smallest
atomic radius.
Be, Si, and P: