Logical Statements

What type of triangle?

why?

If the angles of a triangle are all equal, then you have an equilateral triangle.

A logical argument consists of a premise (hypothesis) and a conclusion.

statements1. If then

hypothesis the "if" part

conclusion the "then" partknown as a "conditional" statement

Symbolism:

p - represents the hypothesis

q - represents the conclusion

p q

This means: if p, then q

Examples:

If the cheque bounced, then there was no money in the account.

2. Converse StatementFormed by interchanging the hypothesis and the conclusion.

If you have an equilateral triangle, then the angles are all equal.

q p

**the converse of a statement may or may not be true.**

3. If and only ifis used when the converse of a true statement is true.

ex. You have an equilateral triangle "if and only if" the angles are all equal.

ex. A triangle has two equal sides "if and only if" it has at least two equal angles.

p q

4. Contrapositivereverse and negate the two parts of the original statement

if you do not have an equilateral triangle, then the angles are not all equal.

5. Inverse statement: you negate the hypothesis and the conclusion, but you don't move them.

If the angles of a triangle are not all equal, then you do not have an equilateral triangle.

If Jeamille lives in Brandon, then Jeamille lives in Manitoba.

Write the converse, inverse, and contrapositive statements. Indicate if true.

2. Converse Statement

Formed by interchanging the hypothesis and the conclusion.

4. Contrapositivereverse and negate the two parts of the original statement

5. Inverse statement: you negate the hypothesis and the conclusion, but you don't move them.