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3A Logic I. Conditional Statements (p→q) If you are driving 80 mph, then you are breaking the law. 1. Converse (q→p) 2. Inverse (~p→~q) 3. Contrapositive (~q→~p) 4. Biconditional (p⇔q) II. Using a conditional statement 5. If two angles form a linear pair, then they are _____. Name__________________________________ 6. Converse (q→p) 7. Inverse (~p→~q) 8. Contrapositive (~q→~p) 9. Biconditional (p⇔q) True False True False True False True False True False III. Conditional Cards Select a statement for the conditional statement. Then select its converse, inverse, and contrapositve. Select a different card for the conditional statement. Then select its converse, inverse, and contrapositve. IV. Segment Addition Postulate 10. What happens when B is between A and C? 11. Given: B is between A and C. Suppose AB=x+1, BC=x+4, and AC=3x–2. What is the value of x? What are the values of AB, BC, and AC? V. Angle Addition Postulate 12. m∠ABC+m∠CBD=m∠_____ 13. Suppose m∠ABD=5x+1, m∠ABC=x+10, and m∠CBD=2x–1. What is the value of x? What are the values of m∠ABD, m∠ABC, and m∠CBD? VI. Logical Conclusions 14. If ∠1 and ∠2 form a linear pair, and ∠1 is obtuse, then …. sur
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15. If two lines, AB and !CD , intersect at P, then ∠APC and ∠BPD …. 16. If a line bisects !AB at point M to form segments !AM and MB , then …. 17. If the sum of two angles of a triangle is less than 90°, then …. VII. Practice 18-­‐22: Given the following conditional statement: If two angles form a linear pair, then they are adjacent. 18. Write the converse. 19. Write the inverse. 20. Write the contrapositive. 21. Write the conditional statement as a biconditional. 22. Consider the truth values of the original, converse, inverse, and contrapositive. Which, if any, are true? Which, if any, are false? Draw a counterexample for any false statements. 23. Claim: If n is even, then n+1 is divisible by 3. Is it true? Or can you find a counterexample? 24-­‐25: Valid or Invalid Arguments. For each of the following examples, decide if the argument is valid or invalid. 24. If someone buys a new Lamborghini, she or he will pay over $200,000. Marie does not buy a new Lamborghini. Therefore Marie does not pay over $200,000 for her new car. 25. In China, job applicants do not ask how much they will be paid when they are hired. When Jin Tai was hired, he asked his employer how much he would be paid. Jin Tai must have been hired outside of China. 26. The following statement is true: If a figure is a triangle, then it is a polygon. Which other statement must also be true? A. If a figure is not a triangle, then it is not a polygon. B. If a figure is not a polygon, then it is a triangle. C. If a figure is a polygon, then it is a triangle. D. If a figure is not a polygon, then it is not a triangle. If an animal is If an animal is
If an animal is If an animal is
not a mouse, not a rodent,
a mouse, then a rodent, then
then it is not a then it is not a
it is a rodent. it is a mouse.
rodent.
mouse.
If the sum of two
angles is 90°,
then the angles
are
complements of
each other.
If two angles are
complements of
each other, then
their sum is 90°.
If the sum of two If two angles are
angles is not
not
90°, then the
complements of
angles are not each other, then
complements of their sum is not
each other.
90°.
If two angles
are congruent,
then their
measures are
equal.
If two angles
have equal
measures,
then the
angles are
congruent.
If two angles
If two angles
are not
have unequal
congruent,
measures,
then their
then the
measures are angles are not
not equal.
congruent.
If m∠A = 28°
then ∠A is an
acute angle.
If ∠A is an
acute angle,
then
m∠A = 28°.
If ∠A is not an
If the measure
acute angle,
of angle A is
then the
not 28°, then
measure of
∠A is not an
angle A is not
acute angle.
28°.
If 2x – 3 = –7,
then x = –2.
If x = –2, then
2x – 3 = –7. If 2x – 3 ≠ –7,
then x ≠ –2.
If x ≠ –2, then
2x – 3 ≠ –7.
If a shape has
If a shape is a
four sides,
rectangle,
then the
then it has
shape is a
four sides.
rectangle.
If a shape is
not a
rectangle,
then the
shape does
not have four
sides.
If a shape
does not have
four sides,
then the
shape is not a
rectangle.
If you are a
teenager,
then you are
at least 13
years old.
If you are at
If you are not If you are less
least 13 years
a teenager,
than 13 years
old, then you then you must old, then you
are a
be less than
are not a
teenager.
13 years old.
teenager.
If she is
responsible
for the money,
then she is
guilty if it is
lost.
If she is not
If she is not
If she is guilty
responsible
guilty if the
if the money is
for the money, money is lost,
lost, then she
the she is not then she is not
is responsible
guilty if it is
responsible
for the money.
lost.
for the money.
If a number is
divisible by 2,
then it is
divisible by 4.
If a number is
divisible by 4,
then the
number is
divisible by 2.
If a number is
not divisible
by 2, then it is
not divisible
by 4.
If a number is
not divisible
by 4, then the
number is not
divisible by 2.