This lesson aims to introduce to you the world of reasoning and logic. Reasoning is one vital skill in studying Mathematics and its vast landscape for learning. Even in real world setting, one can use reasoning to prove or disprove concepts or information. As learner of this lesson, you are expected to achieve the minimum competency for this topic which is to use inductive or deductive reasoning in an argument.

1. LEARNING
OBJECTIVES
At the end of this lesson, you
will be able to:
 provide understanding on the
definition of inductive and
deductive reasoning;
 identify a statement whether it
is inductive or deductive; and

2. INDUCTIVE AND
DEDUCTIVE
REASONING

3. MATH-TIONARY
• Inductive Reasoning – It is the
process of gathering specific
information, usually through
observation and measurement and then
making a conjecture based on the
gathered information.
• Deductive Reasoning – It is the
process of showing that certain

4. Observe the following
statements below.
1. 5, 10, 15, 20, _____. What do you think
is the next number? If you answer 25, then
you are absolutely correct!
2. Adrian wears red t-shirt today.
Yesterday and the other day he also wore
red. What can you say about Adrian? If you
will say Adrian loves red tshirt, then it
could be since he often wears red t-
shirts.
3. My mother is a medical front liner. My
classmates’ mothers are also medical front

5. As defined in our MATH-
TIONARY,
INDUCTIVE REASONING is
the process of gathering
specific information,
usually through
observation and

6. Example 1
Observe the number of circles
in the sequence. What do you
think is the next number of
circles following the last
one?

7. Example 1
Observe the number of circles
in the sequence. What do you
think is the next number of
circles following the last
one?
Think of the pattern you can observe
starting from the 1st 2 circles up to the
last one. From your observation, can you
make a conjecture? What do you think is

8. Example 1
Observe the number of circles
in the sequence. What do you
think is the next number of
circles following the last
one?
For the conjecture, consider the interval of
each term. As one can observe, the interval is
2. It can be assumed that the next term using
the interval is 10. You can also predict for the

9. Example 2
What can you say about the
statements above? Can this be
considered an inductive
reasoning?

10. Example 2
A conjecture is considered a
general statement. This means
that the above statements are an

11. Example 2
But take note, not all statements made through inductive
reasoning are foolproof or always true. Yes, inductive
reasoning is practical since it is from observations or
experience. However, it is not a guarantee or an
automatic acceptance of truth. It must go through a
validity test. Does the conjecture always true in all

12. For example, in the conjecture
made in Example 2. A rectangle is
a square. It can be noted that
rectangles and squares have four
sides and four angles. But a
square has four equal sides,
whereas the rectangle has 2 pairs
opposite sides equal. This
characteristic of rectangle makes
the conjecture invalid.
Just to be clear, inductive reasoning
is practical but not always true in
its conjecture.

14. What have you
observed in the
construction of the
statement? Does it
start with a
specific
information?
The statement
started with a
general information
or an agreed
assumption. “Playing
Mobile Legend may
cause addiction.”

15. How about the
conjecture? The
conjecture is
specifically made.
It is not a general
knowledge, but in a
particular
situation.
This implies that
the statement above
is from a general
information or
agreed assumption
which made a
specific conjecture.

17. Example 1
Suppose that the given statements
are true. Use deductive reasoning to
give a conjecture that must also be
true.
Conjecture: A carabao
has mammary glands.

18. DEDUCTIVE REASONING is
also used in Algebra.
This can be seen during
the process of finding
the value of a variable.
When providing reasons

19. Example 2
Solve the equation for x.
Give a reason for each step
in the process.
Solution:
2 (3x – 5) – 6 = x + 4
6x – 10 – 6 = x + 4 Apply the distributive property.
6x – 16 = x + 4 Combine like terms.
6x – x = 4 + 16 Apply addition property of equality.
5x = 20 Combine like terms.

20. Now, let us do some exercises.
Identify each item whether Inductive
Reasoning or Deductive Reasoning. Put
a check mark (✓) under the
appropriate column.

21. Now, let us do some exercises.
Identify each item whether Inductive
Reasoning or Deductive Reasoning. Put
a check mark (✓) under the
appropriate column.