Let us define the meaning of the five connectives by showing the relationship between the truth
value (i.e. true or false) of composite propositions and those of their component propositions.
They are going to be shown using truth table. In the tables P a
Often we want to discuss properties/relations common to all propositions. In such a case rather
than stating them for each individual proposition we use variables representing an arbitrary
proposition and state properties/relations in terms of th
Sentences considered in propositional logic are not arbitrary sentences but are the ones that are
either true or false, but not both. This kind of sentences are called propositions.
If a proposition is true, then we say it has a trut
Once we have it in this compact form, it is fairly easy to compute S for different values of A, R
and n, though one still has to compute (1 + R)n + 1 . This simple formula represents infinitely
many cases involving all different values of A, R and n. The
Logic is a language for reasoning. It is a collection of rules we use when
doing logical reasoning. Human reasoning has been observed over centuries
from at least the times of Greeks, and patterns appearing in reasoning have
been extracted, abstracted, an
Everyone must have felt at least once in his or her life how wonderful it would be if we could
solve a problem at hand preferably without much difficulty or even with some difficulties.
Unfortunately the problem solving is an art at this poin
One of the most important thing, if not the most important, in the university education is the
cultivation of the ability to extrapolate. Obviously we can not anticipate all the problems you are
going to encounter in the future and prepare you for them. S
This is a find type problem and "working backward" technique is used.
Problem: Given a 4 quart pail and a 9 quart pail, obtain 6 quarts of water in the 9 quart pail
using these two pails. You can fill or empty the pails and you can have as much
This is an example in which you can find a solution once you analyze and understand the
unknowns and data.
Problem: A survey of TV viewers shows the following results:
To the question "Do you watch comedies ?", 352 answered "Yes".,
To the questi
As an example, let us consider a simple problem of investment. Suppose that we invest $1,000
every year with expected return of 10% a year. How much are we going to have after 3 years, 5
years, or 10 years ? The most naive way to find that out would be th
What is Discrete Mathematics ?
Discrete mathematics is mathematics that deals with discrete objects.
Discrete objects are those which are separated from (not connected to/distinct
from) each other. Integers (aka whole numbers), rational numbers (ones that