Let A = {1,2,3}. Determine all the equivalence relations R on A.
For each of these,...
Let A = {1,2,3}. Determine all the equivalence relations R on A.
For each of these, list all ordered pairs in the relation
How many different onto functions f:S→Tf:S→T can be defined that
map the domain S={1,2,3,…,10}S={1,2,3,…,10} to the...
How many different onto functions f:S→Tf:S→T can be defined that
map the domain S={1,2,3,…,10}S={1,2,3,…,10} to the range
T={11,12,13,…,20}T={11,12,13,…,20}? Enter your answer in the box
below.
2. Let A = {a,b} and B = {1,2,3}. (a) Write out all functions f
:...
2. Let A = {a,b} and B = {1,2,3}. (a) Write out all functions f
: A → B using two-line notation. How many different functions are
there, and why does this number make sense? (You might want to
consider the multiplicative principle here). (b) How many of the
functions are injective? How many are surjective? Identify these
(circle/square the functions in your list). 3. Based on your work
above, and what you know about the multiplicative principle, how
many...
2. Let A = {a,b} and B = {1,2,3}.
(a) Write out all functions f :...
2. Let A = {a,b} and B = {1,2,3}.
(a) Write out all functions f : A → B using two-line notation.
How many different functions are there, and why does this number
make sense? (You might want to consider the multiplicative
principle here).
(b) How many of the functions are injective? How many are
surjective? Identify these (circle/square the functions in your
list).
(c) Based on your work above, and what you know about the
multiplicative principle, how many...
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...
How many binary strings of length 15 contain the same
bit in all the odd numbered...
How many binary strings of length 15 contain the same
bit in all the odd numbered positions? The positions are numbered
1, 2, . . . , 15. Show how you arrived at your answer, which rules
of counting were used etc.
Thank You