Tournament System Axiom 1: Every game consists of two players. Axiom 2: For every distinct
pair of players, p and p, there is exactly one game. Axiom 3: There are exactly M players. a.
What are the undefined terms? b. How many games will there be? c. Is the system consistent?
(Show a model for M = 5. Explain what happens each time M increases by 1. 3 points.) d. Is the
system independent? (Your answer requires proof. 3 points.)
Solution
An axiomatic system is a list of undefined terms together with a list of statements (called
“axioms”) that
are presupposed to be “true.” A theorem is any statement that can be proven using logical
deduction
from the axioms.
a.Undefined terms: Games and players
b.Number of games: M-1 (as there are 1 less game than the number of player if they play each
other once)
c.Independence: An axiom is called independent if it cannot be proven from the other axioms. In
other words, the axiom “needs” to be there, since you can’t get it as a theorem if you leave it out.
How do you prove that
something can’t be proved? This relates to the area of mathematics known as logic.
d.Consistency:- If there is a model for an axiomatic system, then the system is called consistent.
Otherwise, the system is inconsistent. In order to prove that a system is consistent, all we need to
do is come up with a model:
a definition of the undefined terms where the axioms are all true. In order to prove that a system
is
inconsistent, we have to somehow prove that no such model exists
For M=5 there are exactly 4 games should be played. Hence there is consistency in the
system.Since this is a definition of the undefined terms where the axioms are all true.
Incoming and Outgoing Shipments in 3 STEPS Using Odoo 17
What is a router Explain in minimum 5 paragraphs can use citatio.pdf
1. What is a router? Explain in minimum 5 paragraphs can use citations
What is a router? Explain in minimum 5 paragraphs can use citations
Solution
Router is a hardware device which is used to recieve packets from other network and also send
the packets to the other network and it is meant to be desingned to work like that. It is mainly
used to share internet to the multiple computers or users to surf the internet. By stepping in to the
latest technologies routers are enormously devoleping so in this context routers are evolved so
ther are two types of routers like wirless routers and connected routers. Connected routers are
used in between the computers and wireless are used to the laptops and mobile phones also.
Routers use headers to forward the packets and use some protocols to transfer the data from
one network to the another network. There are many type of routers that are different in their
physical design some consists of antennas which is used to grab the perfect signal that is sharing
the packets very easily.
The main uses of the router are, These performs the protocol translation, Restricts broadcasts
to the lans, and it acts as a gateway, and calculate or analyse the path to transfer the data and do
more manipulations if any problem occurs in it.
The router mainly functions in the layer 3 even though it functions in all the other layers
basic layer is layer3 where it stands constantly for more period.if you are using a router, your
computer’s IP address is going to begin with either 198.168.0 or 10.0.0. This is because the
powers-that-be decided that those IP address would be reserved for local network use. so in this
way router plays a major role in transferring some important information and need to know the
importance of it.
