Math Tutoring on If-Then Statements, Converse, Contrapositive and Inverse

If-Then Statement:

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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Hook questions:

1.    State the notation:.

2.   State The Converse, Inverse and Contrapositive of an “if-then” Statement.

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