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title: Converse Inverse Contrapositive
---

In Discrete Mathematics, given a conditional statement ”if a,then b”, we
can have 3 related statements:<br>
Any conditional statement is made up of two parts:<br>
i) Hypothesis(”if”):<br>
ii) Conclusion(”then”):<br>
”if a, then b” can be represented as:<br>
a → b<br>
Suppose an example: ”If there is no school, then it is the weekend.”<br>
p → q<br>
• To get the Converse of above conditional statement, interchange hypoth-
esis and the conclusion.<br>
q → p<br>
Hence, the converse will be: ”If it is weekend, then there is no school.”<br>
• To get the Inverse of above conditional statement, take the negation of
both hypothesis and the conclusion.<br>
¬p → ¬q<br>
Hence, the inverse will be: ”If there is school, then it is weekday.”<br>
• To get the Contrapositive of above conditional statement, interchange
the hypothesis and the conclusion of the inverse statement.<br>
¬q → ¬p<br>
Hence, the contrapositive will be: ”If it is weekday, then there is school.”



