This document discusses biconditional statements in mathematics. It defines conditional statements, biconditional statements, and related logical concepts like converse, inverse, and contrapositive. Examples are provided to illustrate these concepts. Students are assigned homework problems analyzing conditional and biconditional statements.

1. 2.2 Biconditional Statements
September 06, 2011
Bellwork
1. What is the definition of conjecture? A guess based on observation
2. Write the next number in the sequence 1, 5, 9, 13,... 17
3. A _______ disproves a conjecture. counterexample
4. (­4)(
7)+2 ­1=?
­27
5. Are you lost yet in chapter 2?
HW pg. 83 #16­25
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2. 2.2 Biconditional Statements
September 06, 2011
2.2 Analyze Conditional Statements
Conditional Statement:
logical statement that has 2 parts-hypothesis
& conclusion
written in if-then form
Ex. If it is raining, then there are clouds in the sky.
Rewrite the conditional statement in if-then form.
All birds have feathers.
If an animal is a bird, then it has feathers.
2 angles are supplementary if they are a linear pair
If 2 angles are a linear pair, then they are
supplementary.
HW: pg 82 #3-5
HW pg. 83 #16­25
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3. 2.2 Biconditional Statements
September 06, 2011
· Conditional statements can be T or F.
· Prove that the conclusion is true every time
the hypothesis is true.
· To show false: give 1 counterexample.
Negation: Opposite of original statement
Original: Ball is red.
Negation: Ball is not red.
Conditional Statement: If m A = 99, then A is obtuse.
T
Converse: exchange the hypothesis and conclusion
If m A is obtuse, then m A = 99.
F
Inverse: negate both the hypothesis and conclusion
If m A ≠99, then A is not obtuse.
F
Contrapositive: write the converse, then negate both hypothesis
and conclusion
If A is not obtuse, then m A ≠ 99.
T
HW pg. 83 #16­25
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4. 2.2 Biconditional Statements
September 06, 2011
HW: pg. 82
#3-5,7-15,31 & 32
HW pg. 83 #16­25
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5. 2.2 Biconditional Statements
September 06, 2011
You can write a definition as a conditional statement
in if-then form or as its converse.
Both are True.
Definition: If 2 lines intersect to form a right
angle, then they are perpendicular lines.
Converse: If 2 lines are perpendicular, then they
intersect to form a right angle.
You can write "line l is perpendicular to line m"
as l m.
l
m
HW pg. 83 #16-18
HW pg. 83 #16­25
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6. 2.2 Biconditional Statements
September 06, 2011
Biconditional Statement:
· When conditional statement and converse are T, then
you can write them as a biconditional statement.
· if and only if (IFF)
· any valid definition can be written as biconditional
HW pg. 83 #16­25
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7. 2.2 Biconditional Statements
September 06, 2011
HW pg. 83 #16­25
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8. 2.2 Biconditional Statements
September 06, 2011
HW pg.83
#16-25
HW pg. 83 #16­25
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