This is a free lesson from our course in Algebra II
In this lesson you'll be introduced to the concepts related to the logical arguments
and making conclusions. Further you'll explore walking through some examples with solution, and the instructor's explanation with the help of audio, video presentation
in own hand writing, how to verify a statement using he truth both "principle
of contradiction" and "principle
of identity". Reasoning is the set of processes that
enables to go beyond the information given and conclusions are based on analysis
of given information. It also helps you to analyze and determine whether an algebraic
statement involving rational/radical
expressions sometimes, always or never true. (More text below video...)
(Continued from above) E.g. You cannot
add any of the given numbers from 3, 6, 9, 12, 15, 18, 21 to get 52, as 52 is not divisible by 3.
Note:
When we arrive at a conclusion using facts, definitions, rule, or properties, it
is called
Deductive Reasoning and a conclusion reached based on deductive
reasoning is always true.
For example: (x x y) x z is the same as (z x
y) x x, is always true. Remember the following steps using the
deductive reasoning here:
Step 1: (x x y) x z = z x (x x y),
using
commutative property of multiplication.
Step 2: = z x (y x x), using commutative property of
multiplication again.
Step 3: = (z x y) x x, using
associative property of multiplication.
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