2.2 – analyze conditional statements. conditional statement hypothesis conclusion logical...
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2.2 – Analyze Conditional Statements
Conditional Statement
Hypothesis
Conclusion
Logical statement written in if-then form. If p, then q.
pq
Statement following the “if”“p” part
Statement following the “then”“q” part
True Statement
False Statement
Counterexample
Assuming “p” is true, the “q” HAS to happen
Assuming “p” is true, the “q” might not happen. You only need ONE example to prove a statement false.
One example that proves a statement is false. When p is true, but q is false.
Converse
Flip the hypothesis and conclusion
If p, then q becomes If q, then p qp
Inverse
Negate the hypothesis and conclusion
If p, then q becomes If not p, then not q ~p ~q
Contrapositive
Negate the hypothesis and conclusion of the converse
If p, then q becomes If not q, then not p ~q ~p
Equivalent to the original statement.
Biconditional statement
Original and converse of a statement are true.
p q AND q p pq
p if and only if q p iff q
1. State the hypothesis and conclusion of the following:
a. If a student studies for a test, then they will get an A in the class.
hypothesis conclusion
1. State the hypothesis and conclusion of the following:
b. If you are a football player, then you are an athlete.
hypothesis conclusion
1. State the hypothesis and conclusion of the following:
c. If x = 3, then x2 = 9.
hypothesis conclusion
2. Rewrite the statement in if-then form. Then write the converse, the inverse, and the contrapositive.
A car runs when there is gas in the tank.
If a car is running, then there is gas in the tank.If-then:
If there is gas in the tank, then the car is running.
Converse:
If the car isn’t running, then there isn’t gas in the tank.
Inverse:
If there isn’t gas in the tank, then the car isn’t running.
Contra:
2. Rewrite the statement in if-then form. Then write the converse, the inverse, and the contrapositive.
All triangles have three sides.
If a polygon is a triangle, then it has 3 sides.If-then:
If a polygon has 3 sides, then it is a triangle.Converse:
If a polygon isn’t a triangle, then it doesn’t have 3 sides.
Inverse:
If a polygon doesn’t have 3 sides, then it isn’t a triangle.
Contra:
3. Rewrite the definition as a biconditional statement.
Two angles are complementary angles when the sum of their measures is 90°
Two angles are complementary angles IFF their sum measures 90°
3. Rewrite the definition as a biconditional statement.
Equilateral polygons have all of their sides congruent.
A polygon is equilateral IFF all of the sides are congruent
4. Determine if the if-then statement is true or false. If false, provide a counterexample.
a. If you drive a mustang, then it is red.
False, You drive a mustang that is black.
b. If m2 = 90°, then it is a right angle.
6. Determine if the if-then statement is true or false. If false, provide a counterexample.
True
c. If A is obtuse, then it measures 155°
6. Determine if the if-then statement is true or false. If false, provide a counterexample.
False, An obtuse angle that is 100°
d. If you stay after school, then you go to math tutorial.
6. Determine if the if-then statement is true or false. If false, provide a counterexample.
False, You stay after school for sports practice
7. Decide whether each statement about the diagram is true. Explain your answer.
mAEB = 90°
False,
No Box!A
B
C
D
E
7. Decide whether each statement about the diagram is true. Explain your answer.
AE + EC = 180°
False,
Segments aren’t measured in degrees!
A
B
C
D
E
7. Decide whether each statement about the diagram is true. Explain your answer.
AED BEC
True,
Vertical AnglesA
B
C
D
E
THE FIRE-FISH STORY“If there is a fire, then a fish dies”
The story must be out of at least 5 conditional statements, ending with “If D, then a fish dies.”
You are to write a creative story consisting entirely of conditional statements. The first statement should be of the form: “If there is a fire, then A.” The second statement should be of the form: “If A, then B.” The hypothesis of each statement must be the conclusion of the previous statement.
If there is a fire, then ___________________________________.
If ________________, then …………………………………
If …………………………., then ***************************************.
If *******************************, then xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx.
If xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx, then a fish dies.
# 19
An angle measures between 90° and 180° IFF it is obtuse
HW ProblemSecti
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#Assignment Spiral ?
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2.2 82-85 1-15 odd, 16-18, 19-25 oddFire-Fish Story
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