This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Disproving Statements
In this section, with the help of some examples, you will learn to use logical reasoning to prove statements that are true and find counter examples to disprove statements that are false.
A statement and its converse say different things. In fact, some true statements have false converse. An ‘if-then’ statement is false, if an example can be found for which hypothesis is true and conclusion is false. Such an example is called a counter example. E.g. the statement “The perimeter of a rectangle can never be an odd number of units.” You know that the perimeter of rectangle is given by 2(l
), where l
is the length and w
is the width of the rectangle. Let us take the values of l
= 7units and w
= 1.5 units, substitute 7 for l
and 1.5 for w
in above formula i.e. 2(7 + 1.5), which gives 17. Therefore, this example is disproving the statement “The perimeter of a rectangle can never be an odd number of units.”
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