Tech Math 1

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VALID ARGUMENT

• Tech Math 1

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Definitions

• The goal of reasoning is to make a valid
  argument.
• An argument is a group of statements consisting
  of two or more premises and a conclusion.
• A premise is a statement that is given or proven
  to be true.

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• In a valid argument, the rules of logic are used
  to go from the premises to the conclusion.
• Some arguments are inductive and some are
  deductive.
• A syllogism is a common deductive argument that
  has two premises and a conclusion.

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Summary of Argument

• Sequence of statements
• Statement 1
• Statement 2
• Therefore, Statement 3.
• Statements 1 and 2 are called premises.
• Statement 3 is called conclusion.

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Examples of Arguments

• It is raining
• It is not snowing
• Therefore, it is raining.
• If x2 then xlt5
• xlt5
• x is an even integer
• Therefore, x2.

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Arguments contd

• Premise indicator terms because, since, and
  for the reason that
• Conclusion indicator terms therefore, thus,
  it follows that, so
• Example
• Sarah will do well in logic because she studies
  and anyone who studies does well in logic

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Arguments

• Sarah will do well in logic because she Sarah
  studies and anyone who studies does well in
  logic
• Sarah studies.
• Anyone who studies does well in logic.
• --------------------------------------------------
  -
• Sarah will do well in logic.

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Law of Detachment

• If p q is a true conditional statement and p is
  true, then q is true.
• Ex. If I pass the test, then I get an A in
  geometry. I passed the test. So I got an A in
  geometry.

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Law of Syllogism

• If p q and q r are true conditional
  statements, then p r is true.
• Ex. If I pass the test, then I get an A in
  geometry. If I get an A in geometry, then I get
  a new car.
• Conclusion. I passed the test so I get a new
  car.

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Examples

• Determine if statement (3) follows from statement
  (1) and (2) by the Law of Detachment or the Law
  of Syllogism. If it does, state which law was
  used. If it does not, write invalid.

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Law of Detachment or Law of Syllogism 1

• 1. If an angle is acute, then it is not obtuse.
• 2. ltABC is acute.
• 3. ltABC is not obtuse.
• Valid by Law of Detachment

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Law of Detachment or Law of Syllogism 2

• 1. If you save a penny, then you have earned a
  penny.
• 2. Art saves a penny.
• 3. Art has earned a penny.
• Valid by Law of Detachment.

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Law of Detachment or Law of Syllogism 3

• 1. If you are a teenager, then you are always
  right.
• 2. If you are always right, then people will
  listen to you.
• 3. If you are a teenager, then people will
  listen to you.
• Valid by Law of Syllogism.

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Example 1

• If Hank applies for the job, then he will be the
  new lifeguard at the pool. If he is the new
  lifeguard at the pool, then he will buy a new
  car. Hank applies for the job.
• Conclusion?
• Hank will buy a new car.
• Law of Syllogism

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Example 2

• If two planes intersect, then their intersection
  is a line. Plane A and plane B intersect.
• Conclusion?
• Plane A and plane B intersect in a line.
• Law of Detachment

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Example 3

• If you cut class, then you will receive a
  detention. You cut class.
• Conclusion?
• You received a detention.
• Law of Detachment

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Example 4

• If Jay doesnt work hard, then he wont start the
  game and will quit the team. Jay quit the team.
• Conclusion?
• No conclusion. We do not why he quit the team.