Download 5 Conditional Statements and their Converse.notebook

5 Conditional Statements and their Converse.notebook
March 23, 2016
What are conditional statements?
Conditional statements are statements in the form..
Unit 2
Lesson 5
Conditional Statements &
Their Converse
"If P, then Q..."
• P is a hypothesis (condition)
• Q is a conclusion (consequence)
Example:
"If it is Saturday, then it is the weekend"
Aug 25­1:40 PM
Jan 7­3:30 PM
How do you verify a conditional statement to see if it is true? Types of statements:
The hypothesis (P) and the conclusion (Q), are either true or false...so 4 cases must be considered. Use a "truth table" to help.
1. A Converse Statement is a conditional statement in which the hypothesis and the conclusion are switched.
1. If P and Q are both true,
the statement is true.
2. If P and Q are both false,
the statement is still true.
3. If P is false and Q is true,
the statement is still true.
4. If P is true and Q is false,
the statement is false.
Jan 7­3:31 PM
2. A Biconditional Statement is written when a conditional statement and its converse are both true. We use special notation iff meaning "if and only if", and the format of:
P iff Q.
Example:
Conditional:
Converse:
If P, then Q.
If Q, then P.
Conditional:
If a polygon's internal angles sum to 180 degrees, then the polygon is a triangle.
True!
Example:
Conditional:
If it is Saturday, then it is the weekend.
Converse:
If it is the weekend, then it is Saturday.
Converse:
If a polygon is a triangle, then the polygon's internal angles sum to 180 degrees.
True!
Biconditional: A polygon's internal angles sum to 180 degrees
if and only if (iff) the polygon is a triangle.
Jan 7­3:35 PM
Jan 7­3:56 PM
Jan 7­4:03 PM
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5 Conditional Statements and their Converse.notebook
Counterexamples:
A counterexample is an example that shows a statement to be false.
Example:
Statement:
March 23, 2016
Example 1:
Example 2:
Conditional Statement:
Conditional Statement:
If you live in Fredericton, then you live in New Brunswick. If you are in Mr. Murdock's math class, then your classroom has no windows. If a shape has 4 sides, then it is a rectangle.
Counterexample: a rhombus
Converse:
Converse:
Biconditional Statement: (If not, provide a counterexample)
Biconditional Statement: (If not, provide a counterexample)
Jan 14­9:56 AM
Oct 27­10:35 AM
Practice
Example 3:
Oct 27­10:35 AM
4. If a shape is a square, then the shape has four equal sides. Write the converse of each of the following statements. If the converse is true, then write the biconditional statement. If either the conditional statement or the converse is false, provide a counterexample. Conditional Statement:
If a polygon has 4 sides, then the polygon is a quadrilateral. 1. If x = 3, then x2 = 9. Converse:
5. If the equation of a line is y = 2x + 5, then the slope of the line is 2. 2. If x = ­ 4, then | x | = 4. Biconditional Statement: (If not, provide a counterexample)
3. If n is an even number, then n + 1 is an odd number.
Jan 14­9:24 AM
Oct 27­10:21 AM
Oct 27­10:51 AM
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5 Conditional Statements and their Converse.notebook
March 23, 2016
6. If a triangle has three equal angles, then the triangle is an equilateral triangle. 7. If two triangles are similar, then the corresponding angles of the two triangles are equal. Oct 27­10:52 AM
Jan 14­9:35 AM
Jan 14­9:41 AM
Mar 17­8:32 PM
Mar 17­8:41 PM
p. 203 Q 1­3, 5, 6, 8, 10
Mar 17­8:48 PM
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5 Conditional Statements and their Converse.notebook
March 23, 2016
Mar 17­8:41 PM
Mar 17­8:43 PM
Mar 17­8:44 PM
Mar 17­8:45 PM
Mar 17­8:43 PM
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