This document defines and explains key concepts in logic and reasoning. It discusses logic as the study of distinguishing correct from incorrect reasoning. It then defines reasoning as using a systematic process of steps and given statements to arrive at a conclusion. It discusses the difference between sentences and propositions, and types of propositions like compound, conjunctive, disjunctive, and conditional propositions. The document also defines deductive and inductive arguments, and how to indicate the type of argument being made.

1. Logic

2. Logic
Logic is the study of methods, principles, and
techniques used to distinguish correct from bad
reasoning.

3. Logic
• Some apples are red. Therefore it follows
that President Obama was actually born in
the old Soviet Union, which makes him
ineligible to be President of the United
States.

4. Reasoning
 The process of using a rational, systematic series of
steps based on sound procedures and given
statements to arrive at a conclusion.
 A special kind of thinking in which problems are
solved, in which inference takes place., that is, in
which conclusions are drawn from premises.

5. Reasoning
Inference /Conclusion
 Refers to the process by which one proposition is arrived at
and affirmed on the basis of one or more other propositions
accepted as the starting point of the process.

6. Propositions/Statement
 A claim/statement that either affirms or denies
something or is either true or false.
 Although its truth or falsity may be unknown.

7. Preposition
• For example
– “There is life on some other planet in our
galaxy”

8. Proposition
• Do you know how to play chess?
– Question assert nothing, therefore it is not
proposition

9. Proposition
• Proposition is the term we use to refer to
what it is that declarative sentences are
typically used to assert.
• For Example
– It is raining

10. Continued…
 Difference between sentence and proposition
 A sentence is always a sentence in a particular language, the
language in which it is used. Propositions is not peculiar to a
language.
 Exactly the same sentence, in different contexts, may be used
to make different propositions.
Example:
– The present president of Pakistan is an army chief.
General Zai-ul-Haq in 1980s
General Pervez Musharraf in 2002

11. Proposition/Sentence
• “The largest state in the United States was
once an independent republic”
– “once” expressed a true statement or
proposition (about Texas)
– but if asserted today would express a false
statement or proposition (about Alaska)
– The same words assert different propositions
at different times.

12. Proposition
• Compound Proposition
– containing other propositions within
themselves
– For Example
• The Amazon Basin produces roughly 20 percent of
the Earth’s oxygen, creates much of its own
rainfall, and harbors many unknown species.
– In above sentence we have three Proposition
» What it produce
» What it create
» What it harbors
–

13. Proposition
• Conjunctive Proposition
– The conjunctive proposition is one which
asserts that two alternatives cannot be true at
the same time. (It is possible for both
alternatives to be false.)
– For Example
• “Canada is in North America and New York City is
the biggest city in Canada”.
• From above example it is clear that, if either one of
the individual propositions are False, then the
whole thing is False. And since we know that one
is False, indeed the whole thing is taken as False

14. Proposition
• Disjunctive Proposition
– It presents two or more alternatives, one of
which is true. Its members are linked by the
conjunctions “either…or”
– For Example
• "Canada is in North America or New York City is
the biggest city in Canada.“
• Now we have one proposition that is True, so the
whole thing is seen as True.

15. Proposition
• Conditional Proposition
– In this type of proposition one clause asserts
something as true provided that the other
clause is true
• The first clause is “if”
• The second one is “then”
• For Example
– If strong typhoons come, then crops will be destroyed

16. Argument
• An argument is one or more statements,
called premises, offered as a reason to
believe that a further statement, called the
conclusion, is true, that is, corresponds to
reality.
• To tell your audience that you are drawing
your conclusion, introduce your statement
using a word or phrase such as
“therefore,” “in conclusion,” “thus,”

17. Argument
• For Example
– No one was present when life first appeared
on earth. Therefore any statement about life’s
origins should be considered as theory, not
fact
– Premise: No one was present when life first
appeared on earth
– Conclusion: Therefore any statement about
life’s origins should be considered as theory,
not fact.

18. Deductive Argument
• A deductive argument is an argument in
which it is thought that the premises
provide a guarantee of the truth of the
conclusion.
• In a deductive argument, the premises are
intended to provide support for the
conclusion that is so strong that, if the
premises are true, it would be impossible
for the conclusion to be false.
• in deductive argument we move from

19. Deductive Argument
• You can tell your audience that your
argument is deductive by introducing your
conclusion with wording such as “therefore
it must be that,” or “it necessarily follows
that,” or “therefore it is certain that,” or “it is
conclusively proven that,” and so on.
These phrases are called “deductive
indicators.”

20. Inductive Argument
• An inductive argument is an argument in
which it is thought that the premises
provide reasons supporting the probable
truth of the conclusion.
• In an inductive argument, the premises are
intended only to be so strong that, if they
are true, then it is unlikely that the
conclusion is false.
• For Example
– The members of the Williams family are

21. Inductive Argument
• You tell your audience that your argument
is inductive by introducing your conclusion
with wording such as “therefore it is
probably the case that,” or “it is likely that,”
or “therefore it is reasonable to conclude
that,” and so on. These phrases are called
“inductive indicators.”