Mathematical Reasoning
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Mathematical reasoning is a topic in which we determine the truth values of statements. There are two types of reasonings--inductive and deductive. We shall be studying about deductive reasoning in this wiki.
Introduction
Before we begin deductive reasoning, we first need to understand the meaning of statements. Statements are anything which are always true or always false. Those sentences which are true sometimes and false other times are not considered statements.
I ate an icecream on Monday.
The above sentence cannot be considered a statement, because it is not true for all Mondays. If I ate an icecream on Monday 13, it is not necessary that I would eat it on Monday 20. So, as this sentence is neither true all the times nor false all the times, this sentence is not considered a statement. \(_\square\)
A positive multiple of 2 is \(\geq\) 2.
Since the above sentence is true all the times, it is considered as a statement. \(_\square\)
The sun rises in the west.
Since the above statement is false all the times, it is considered as a statement. \(_\square\)