Math Tutoring on If-Then Statements, Converse, Contrapositive and Inverse
If ‘p’, then ‘q’ is an “if-then”statement, where ‘p’ is called the Hypothesis or Antecedent and ‘q’ is called the Conclusion or Consequent.
An “if-then” statement is called a Conditional Statement. Conditional Statements sometimes are expressed without the word “if” and “then” but can always be restated using “if” and “then”.
Various forms of conditional Statements:
1. If ‘p’, then ‘q’. e.g. .
2. ‘p’ implies ‘q’. e.g. .
3. ‘p’only if ‘q’. e.g. .
4. ‘q’ if ‘p’. e.g. .
The Converse of an if-then Statement
When the Hypothesis and Conclusion of an “if-then”Statement are interchanged, the new statement is called the Converse of the original “if-then” statement. The Converse of a ‘true’ statement, can be ‘true’ or ‘false’.
Statement: if p, then q. E.g. If it is raining, then it is cloudy.
Converse: if q, then p. E.g. If it is cloudy, then it is raining.
Contrapositive and Inverse of an if-then statement:
Statement: if p, then q.
Contrapositive: If not q, then not p.
Inverse: if not p, then not q.
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1. State the notation:.
2. State The Converse, Inverse and Contrapositive of an “if-then” Statement.
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