Algebra II: Algebriac statement sometime, always or never true
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.
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(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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