2. Thinking Critically Discussion 1 web 1 world 41. Campaign Site
42. Gun Control Debate
43. Death penalty Debate
44. Health Care Debate
45. Fallacy Web Sites
1 world
46. Editorial Fallacies
47. Fallacies in Advertising
48. Fallacies in Politics
49. Personal Fallacies
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3. Propositions and Truth Values
Unit 1B
Propositions and Truth Values
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4. Definitions
A proposition makes a claim (either an assertion or a denial) that may be either true or false. It must have the structure of a complete sentence.
Any proposition has two possible truth values: T = true or F = false.
A truth table is a table with a row for each possible set of truth values for the propositions being considered.
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5. Negation (Opposites)
The negation of a proposition p is another proposition that makes the opposite claim of p.
← If p is true (T), not p is false (F).
← If p is false (F), not p is true (T).
Symbol: ~
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6. Negation CN 1a-b
1.Consider the proposition – Betsy is the fastest runner on the team.
a. Write its negation.
b. If the negation is false, is Betsy really the fastest runner on the team?
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7. Double Negation
The double negation of a proposition p, not not p, has the same truth value as p.
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8. Radiation and Health CN 2
After reviewing data showing an association between low-level radiation and cancer among older workers at the Oak Ridge National Laboratory, a health scientist from the U of North Carolina was asked about the possibility of a similar association among younger workers at another national laboratory. He was quoted as saying: My opinion is that it’s unlikely that there is no association.
2. Does the scientist think there is an association between low-level radiation and cancer?
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9. The 2000 Miranda Ruling CN 3
In a June 2000 decision, the US Supreme Court voted 7-2 to uphold the basic requirements of the 1966 Miranda decision. That decision required that suspects taken into custody be informed of their constitutional rights, such as the right to remain silent and the right to legal counsel. In his majority opinion, Chief Justice William Rehnquist wrote: …legal principles weigh heavily against overruling Miranda now.
3. According to this statement, did the Chief Justice feel that legal principles support or oppose the original Miranda decision?
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10. Logical Connectors
Propositions are often joined with logical connectors—words such as and, or, and if…then.
Example:
p = I won the game.
q = It was fun.
Logical Connector
and or
if…then
New Proposition
I won the game and it was fun.
I won the game or it was fun.
If I won the game, then it was fun.
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11. And Statements (Conjunctions)
Given two propositions p and q, the statement p and q is called their conjunction. It is true only if p and q are both true.
Symbol:
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12. And Statements CN 4
4. Evaluate the truth value of the following two statements:
a. The capital of France is Paris and Antarctica is cold.
b. The capital of France is Paris and the capital of America is Madrid.
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13. Or Statements (Disjunctions)
The word or can be interpreted in two distinct ways:
An inclusive or means “either or both.”
An exclusive or means “one or the other, but not both.”
In logic, assume or is inclusive unless told otherwise.
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14. Inclusive or Exclusive CN 6
Kevin’s insurance policy states that his house is insured for earthquakes, fire, or robbery. Imagine that a major earthquake levels much of his house, the rest burns in a fire, and his remaining valuables are looted in the aftermath.
6. Would Kevin prefer that the or in his insurance policy be inclusive or exclusive? Why?
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15. Or Statements (Disjunctions)
Given two propositions p and q, the statement p or q is called their disjunction. It is true unless p and q are both false.
Symbol:
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16. Smart Cows? CN 7
Consider the statement: Airplanes can fly or cows can read.
7. Is it true?
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17. Key Word Search CN 8
You are doing a research report for which you need to find articles about the federal debt that appeared in either Time or Newsweek between 2008 and You have access to a database that allows you to search on date, magazine, and title.
8. How should you structure the search?
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18. If… Then Statements (Conditionals)
A statement of the form if p, then q is called a conditional proposition (or implication). It is true unless p is true and q is false.
Proposition p is called the hypothesis.
Proposition q is called the conclusion.
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19. Conditional Truths CN 9 9. Evaluate the truth of the statement:
If = 5, then = 4
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20. Truth Table Practice Note: ~ signifies NEGATION
 signifies AND
 signifies OR
Practice by writing the truth values of each row in the table above.
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21. Truth Table Practice Note: ~ signifies NEGATION
 signifies AND
 signifies OR
Practice by writing the truth values of each row in the table above.
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22. Truth Table Practice Note: ~ signifies NEGATION
 signifies AND
 signifies OR
Practice by writing the truth values of each row in the table above.
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23. Truth Table Practice Note: ~ signifies NEGATION
 signifies AND
 signifies OR
Practice by writing the truth values of each row in the table above.
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24. Truth Table Practice Note: ~ signifies NEGATION
 signifies AND
 signifies OR
Practice by writing the truth values of each row in the table above.
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25. Alternative Phrasings of Conditionals
The following are common alternative ways of stating if p, then q:
p is sufficient for q
p will lead to q
p implies q
q is necessary for p
q if p
q whenever p
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26. Rephrasing Conditional Propositions CN 10a - c
Recast each of the following statements in the form if p, then q. Discuss whether the statement is true of false.
a. A rise in seas level will devastate Florida
b. A red tag on an item is sufficient to mean it’s on sale.
c. Being male is necessary for being president of the United States.
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27. Variations on the Conditional
Converse:
Inverse:
Contrapositive:
If it is raining, then I will bring an umbrella to work.
If I bring an umbrella to work, then it must be raining.
If it is not raining, then I will not bring an umbrella to work.
If I do not bring an umbrella to work, then it must not be raining.
If p, then q
If q, then p
If ~p, then ~q
If ~q, then ~p
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28. Logical Equivalence
Two statements are logically equivalent if they share the same truth values.
logically equivalent
logically equivalent
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29. Logical Equivalence CN 11a-c
Consider the statement
If a creature is a whale, then it is a mammal.
a. Write its converse, inverse, and contrapositive.
b. Evaluate the truth of each statement.
c. Which statements are logically equivalent?
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30. 1B Homework 1A Discussion Paragraph (DP) Class Notes (CN) 1-11
P.31 Quick Quiz 1-10
p. 31: 1-12
1 web
103. Web Searches
1 world
104. Logical Or
105. Multiple Negation
106. Conditional News
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