In this section, with the help of some examples, you'll 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 'ifthen' 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 + w),
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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