DEDUCTIVE REASONING
AND INDUCTIVE REASONING
DEDUCTIVE REASONING
is a procedure in which
conclusions are logically formed from
given information. It works from general
to specific and considered as the most
valid form of proof.
DEDUCTIVE REASONING-
Deductive Reasoning is composed of
two statements called PREMISES
and produces a deduction called
CONCLUSION.
TWO LAWS OF DEDUCTIVE REASONING:
LAW OF DETACHMENT : If p is true then q is true,
p
q is true statement.
LAW OF SYLLOGISM: If p
q and q r are true
statements then p r is a true statement.
EXAMPLE: LAW OF DETACHMENT
PREMISES: All 9 students are taking geometry.
James is a grade 9 student.
CONCLUSION: James is taking Geometry.
Example: LAW OF SYLLOGISM OR TRANSITIVITY
PREMISES: If you are a grade 9 student, then you
are taking Geometry.
If you are taking Geometry, then you will
be good in reasoning.
CONCLUSION : If you are a grade 9 student, then
you will be good in reasoning.
Decide whether the argument is VALID OR
INVALID.
Kath is in the canteen or in the library.
Kath is not in the canteen.
Therefore, Kath is in the library.
VALID
Some math club officers are boys.
Justine is a Math Club officer.
Therefore, Justine is a boy.
invalid
Solution: though it is true
that Justine is a math club
officer but justine could be
a girl.
All math club officers are boys.
Justine is a Math club officer.
Therefore, Justine is a boy.
VALID
Solution: Since all math club
officers are boys and math
club officer, it follows that
Justine is a boy.
If an animal is a bird, then it has wings.
If an animal has wings, then it can fly.
Therefore, if an animal is a bird, then it
can fly.
inVALID
Decide whether the
argument is VALID OR
INVALID.
1. All birds can fly.
An ostrich is a bird.
Therefore, an ostrich can fly.
2. If 3x = 15, then x = 5
x ≠ 5.
Therefore, 3x ≠ 15
3. If a student violates a school policy, then he or she will be sent
to guidance office.
If a student will be sent to guidance office, then his or her
parents will be called.
Therefore, If a student violates a school policy, then his or her
parents will be called.
INDUCTIVE REASONING
INDUCTIVE REASONING is a procedure
where data are observed, patterns are
recognized and conclusions are based on
the observations made. The generalization
used in inductive reasoning is called
conjecture.
• Most scientific and mathematical
inquiry begins with inductive reasoning.
Solving patterns whether visual pattern
or number pattern and finding a general
rule is part of inductive reasoning.