This document provides an overview of logical reasoning and different types of logical statements. It defines conditional, converse, inverse, and contrapositive statements and provides examples of each. It also discusses deductive reasoning through syllogisms and inductive reasoning. Key points include: - Conditional, converse, inverse, and contrapositive statements relate to whether a statement is true or false. - Deductive reasoning uses existing facts to deduce new conclusions through syllogisms with a major premise, minor premise, and conclusion. - Inductive reasoning observes patterns in data to form generalizations and conjectures. It was used in ancient geometry to solve practical problems.

1. INTRODUCTION
LOGICAL REASONING
Lesson Plan of:
Lorena M. Masbaño

2. GEOMETRY

3. GEOMETRY

4. GEOMETRY

5. GEOMETRY
comes from the two Greek
words:
Geo - “earth”
Metri-“Measurement”.

6. GEOMETRY
deals with shapes that we see
in the world each day

7. Euclid
An ancient
Greek
philosopher
who first
developed
Geometry
around 300
B.C.

8. Elements
this is the
book of Euclid
which contains
the
fundamentals
and concepts
in Geometry.

9. Thoughts to ponder:
 What do you think will happen if
Geometry was not discovered or
introduced to the World?
•What would its effects to the
infrastructure? to houses? to
businesses?

10. RH BILL

11. RH BILL
1. Who among you have heard
or read anything about the
issue on RH Bill?

12. RH BILL
2. What do you know about
the said issue?

13. RH BILL
3. What is your stand about
the Bill? Are you pro-RH Bill?
Or are you against it?
4. Why do you say so?

14. Every time we expressed an
argument, we used
statements that would really
hit the idea that we want to
express.

15. That is why we need to think
carefully and logically so
that the statement would be
accepted as true.

16. LOGICAL REASONING
Conditional Statement
p q
has two parts: a hypothesis
denoted by p, and a
conclusion, denoted by q.

17. EXAMPLE 1:
Glass objects are fragile.
Conditional:
If the objects are made of
glass, then they are fragile.
(TRUE)

18. LOGICAL REASONING
Converse Statement:
-“If q, then p” is written as
q p

19. EXAMPLE 1:
Glass objects are fragile.
Converse:
If the objects are fragile, then
they are made of glass. (FALSE)

20. LOGICAL REASONING
Inverse Statement:
- “If not p, then not q” is
written as ~ p ~ q

21. EXAMPLE 1:
Glass objects are fragile.
Inverse:
If the objects are not made of
glass, then they are not fragile.
(FALSE)

22. LOGICAL REASONING
Contrapositive Statement:
- “If not q, then not p” is
written as ~ q ~ p

23. EXAMPLE 1:
Glass objects are fragile.
Contrapositive:
If the objects are not fragile, then
they are not made of glass.
(FALSE)

24. LOGICAL REASONING
Biconditional:
is form when a conditional
and its converse are both
true.
In symbols: “p if and only if q”
is written as p q

25. EXAMPLE 1:
Glass objects are fragile.
Biconditional:
No biconditional statements can
be drawn since the converse
statement is false.

26. For BICONDITIONAL:
ORIGINAL: Mammals have
mammary glands
CONDITIONAL: If an animal
is a mammal, then it has a
mammary gland. (TRUE)

27. For BICONDITIONAL:
CONVERSE: If an animal has
mammary gland, then it is a
mammal. (TRUE)
BICONDITIONAL: An animal
is a mammal if and only if it
has a mammary gland. (TRUE)

28. Conditional statement
may be true or false. To show
that a conditional statement
is TRUE, you must construct
a logical argument using
reasons.

29. 1. Definition- a statement of
a word, or term, or phrase
which made use of
previously defined terms
2. Postulate- is a statement
which is accepted as true
without proof.

30. 3. Theorem- is any statement
that can be proved true.
4. Corollary- to a theorem is a
theorem that follows easily
from a previously proved
theorem.

31. EXAMPLE 2:
Complementary angles are any two
angles whose sum of their measure
is 90.
CONDITIONAL: If two angles
are complementary, then the
sum of their measure is 90 .
TRUE

32. CONVERSE: If the sum of the
measures of two angles is
90, then they are
complementary. TRUE
BICONDITIONAL: Two angles
are complementary if and
only if the sum of their
measure is 90. TRUE

33. INVERSE: If two angles are
not complementary, then the
sum is not . TRUE
CONTRAPOSITIVE: If the
sum of the measures of two
angles is not 90, then they are
not complementary. TRUE

34. EXAMPLE 3:
The sum of two odd numbers is
even.
CONDITIONAL: If two
numbers are odd, then their
sum is even. TRUE
CONVERSE: If the sum of two
numbers is even, then they
are odd numbers. TRUE

35. BICONDITIONAL: Two
numbers are odd if and only
if their sum is even. TRUE
INVERSE: If two numbers are
even, then their sum is odd.
FALSE

36. CONTRAPOSITIVE: If the
sum of the numbers is
odd, then they are odd
numbers. FALSE

37. DEDUCTIVE REASONING
-from deduce means to reason
form known facts;
-use in proving theorem;
-using existing structures to
deduce new parts of the
structure.
-“if a, then b”

38. SYLLOGISM
- an argument made up of three
statements: a major premise, a
minor premise (both of which
are accepted as true), and a
conclusion.

39. EXAMPLES OF SYLLOGISM:
Major Premise: If the
numbers are odd, then their
sum is even.
Minor Premise: The numbers
3 and 5 are odd numbers.
Conclusion: the sum of 3 and
5 is even.

40. EXAMPLES OF SYLLOGISM:
Major Premise: If you want
good health, then you should
get 8 hours of sleep a day.
Minor Premise: Aaron wants
good health.
Conclusion: Aaron should get
8 hours of sleep a day.

41. EXAMPLES OF SYLLOGISM:
Major Premise: Right angles
are congruent.
Minor Premise: ∟1 and ∟2
are right angles.
Conclusion: ∟1 and ∟2 are
congruent.

42. EXAMPLES OF SYLLOGISM:
Major Premise: Diligent
students do their homeworks.
Minor Premise: Amy and
Andy are diligent students.
Conclusion: Amy and Andy do
their homeworks.

43. INDUCTIVE REASONING:
It is a process of observing
data, recognizing
patterns, and making
generalizations from
observations.

44. Geometry is rooted in
inductive reasoning. The
geometry of ancient times
was a collection of
procedures and
measurements that gave
answers to practical
problems.

45. Used to calculate land areas,
build canals, and build
pyramids.
Using inductive reasoning to
make a generalization called
conjecture.

46. Use inductive reasoning to find the
next term/figure of each sequence.

49. THE END