This lesson explains the concepts of Inductive and Deductive Reasoning
and about using them. You’ll learn the related content, explanations and including
practice problems with solution in the presentation by instructor using video and
in own hand writing. This will help you to apply the developed skills for finding
solution to real-world problems.
Inductive reasoning is a process with logical argument which does not prove a
statement, but rather assumes it. It generally looks for patterns and making conjectures.
Here the expression conjecture means an unproven statement based on observation. As it has
the factor of uncertainty, inductive reasoning should be avoided where possible, while proving
geometric properties.
(More text below video...)
(Continued from above)
As noted above, simply observing a number of situations in which a pattern exists
doesn't mean that this may be true for all situations. However; a hypothesis based
on inductive reasoning, can form the basis for more careful study of a situation.
E.g. if you observe that in a few given rectangles, the diagonals are congruent,
you may inductively reason and say: diagonals of the rectangles are congruent.
Generally it may be true, but it is not proved through the limited observations.
Further, this hypothesis can be tested and applied using other ways and come out
with a theorem i.e. proven statement.
Deductive Reasoning means reaching a conclusion by combining known truths create
certainty and conclude truths i.e. it has a valid form of proof. In order to use
deductive reasoning there must be a starting point, say the axioms or postulates.
For example, an axiom in geometry asserts that given two points there is only one
line which can contain both points. Observe that while this is an axiom, it can be
used to deduce that two different lines intersect at most at one point.
The reasons you can use to justify the statements in proof can be like:
• given/available information
• definitions
• postulates
• theorems proved earlier
Notice that the relevant axioms or postulates used are considering the
involved relationship. For example, given that a certain quadrilateral is
a rectangle, and that all rectangles have equal diagonals, you’ll deduce that the
diagonals of the given are equal. When deductive reasoning leads to distorted
conclusions, may be due to the reasons like - that the premises were incorrect
or all the relevant properties were not considered while concluding.
The difference mainly between inductive and deductive reasoning is
the way arguments are expressed. Notwithstanding the inductive argument can be
expressed deductively, as also any deductive argument can be expressed inductively.
Remember: Inductive reasoning is the process of arriving at a conclusion based on
a set of observations, and as such it is not a valid method of proof.
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