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