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