First slide

Introduction to mathematical reasoning

Question

Which of the following is the contrapositive of 'If two triangles are identical, then these are similar'?

Moderate

A

If two triangles are not similar, then these are not identical
B

If two triangles are not identical, then these are not similar
C

If two triangles are not identical, then these are similar
D

If two triangles are not similar, then these are identical

Solution

Consider the following statements
p: Two triangles are identical.
q: Two triangles are similar.
$Clearly, the given statement in symbolic form is p \Rightarrow q .$
$Therefore, its contrapositive is given by ~ q \Rightarrow\sim p$
$Now, ~ p : two triangles are not identical.$
$~ q : two triangles are not similar.$
$∴ ~ q \Rightarrow\sim p : If two triangles are not similar, then these are not identical$

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