Question

Consider these relations on the set of integers

R_{1} = { (a,b) | a < b or a ≥ b}

R_{2} = { (a,b) | a + b < 5 }

R_{3} = { (a,b) | a <= b }

R_{4} = { (a,b) | a = b +3 }

R_{5} = { (a,b) | a < b - 1 }

R_{6} = { (a,b) | a + 2 > b }

Choose following pairs that fit at least four or more of above 6
relations (R_{1} to R_{6}) ? ( Choose all answers
that apply.)

Group of answer choices

(0, 3)

(2, 5)

(4, 6)

(4, 7)

(2, -2)

(7, 4)

(1, 1)

Answer #1

consider a 4 out of 5 system such that r1=0.96, r2=0.98,
r3=0.93, r4=0.99 and r5=0.94. compute system reliability.

Consider a system with eight resources currently allocated as
follows:
Resource
Allocated to Process
R1
P4
R2
P1
R3
P5
R4
P7
R5
P2
R6
P8
R7
P3
R8
P6
The following sequence of additional resource requests is then
processed. (Let REQ(A,B) denote process A's request for resource
B.)
REQ(P4, R2)
REQ(P3, R6)
REQ(P2, R1)
REQ(P7, R7)
REQ(P6, R1)
REQ(P5, R7)
The above sequence of requests do not cause a deadlock. Verify
this fact by constructing a resource-allocation graph involving...

Given a relation R(A, B, C, D, E) with the following FD
Set
FD = { A→C, B→C, C→D, DE→A, CE→A}
Suppose we decompose it into R1(A, D), R2(A, B), R3(B, E), R4(C, D,
E) and R5(A, E), is it a lossless decomposition? Show your
proof.

Problem 3
For two relations R1 and
R2 on a set A, we define the
composition of R2 after R1
as
R2°R1 = { (x,
z) ∈ A×A | (∃ y)( (x,
y) ∈ R1 ∧ (y, z) ∈
R2 )}
Recall that the inverse of a relation R, denoted
R -1, on a set A is defined as:
R -1 = { (x, y) ∈
A×A | (y, x) ∈ R)}
Suppose R = { (1, 1), (1, 2),...

Consider the following spot interest rates for maturities of
one, two, three, and four years. r1=3.57% r2=3.79% r3=3.1% r4=4.26%
If inflation in year 3 (that is, between the end of year 2 and end
of year 3) is expected to be 2.02 percent, what real rate (in
percent) does this imply for year 3?

For each of the following relations on the set {1, 2, 3, 4}
(a) { (1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (2,
3), (2, 4), (3, 3), (3, 4), (4, 4) }
(b) { (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)
}
(c) { (2, 4}, (4, 2) }
(d) ( (1, 3), (1, 4), (2, 3), (2, 4), (3, 1), (3, 4)
}
Choose all answers that apply.
Group of...

Consider the following relation ∼ on the set of integers
a ∼ b ⇐⇒ b 2 − a 2 is divisible by 3
Prove that this is an equivalence relation. List all equivalence
classes.

Give an example of each if possible, if not possible tell
why.
1) A set of non-zero vectors in R4 that span R4 but are not
linearly independent
2) A linear transformation T: R3 -> R3 that is one to one but
NOT onto
3) A Linear transformation T: R3 -> R4 that is one to one
4) A Linear transformation T: R4 -> R3 that is onto
5) A Linear transformation T: R3 -> R4 that is onto

A.)
Consider the following spot interest rates for maturities of
one, two, three, and four years.
r1 = 5.3% r2
= 5.9% r3 = 6.6%
r4 = 7.4%
What are the following forward rates, where f1,
k refers to a forward rate for the period beginning in one
year and extending for k years? (Do not round
intermediate calculations. Enter your answers as a percent rounded
to 2 decimal places.)
B,)
Consider the following spot interest rates for maturities...

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, ...

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