1. Logical Statements

2. What type of triangle?
why?
If the angles of a triangle are all equal, then
you have an equilateral triangle.

3. A logical argument consists of a premise
(hypothesis) and a conclusion.
1. If then statements
hypothesis the quot;ifquot; part
conclusion the quot;thenquot; part
known as a quot;conditionalquot; statement

4. Symbolism:
p ­ represents the hypothesis
q ­ represents the conclusion
p ­­> q
This means: if p, then q

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

6. 2. Converse Statement
Formed 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.**

7. 3. If and only if p < ­­ > q
is used when the converse of a true
statement is true.
ex. You have an equilateral triangle quot;if
and only ifquot; the angles are all equal.
ex. A triangle has two equal sides quot;if and only
ifquot; it has at least two equal angles.

8. 4. Contrapositive
reverse and negate the two parts of the
original statement
if you do not have an equilateral triangle,
then the angles are not all equal.

9. 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.

10. If Jeamille lives in Brandon, then Jeamille
lives in Manitoba.
Write the converse, inverse, and
contrapositive statements. Indicate if true.