Chapter 20: Simple and Compound Statements

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Chapter 20Simple and Compound Statements
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Compound Statements (pp. 202-207)

• A compound statement contains another statement
  as a proper part.
• Nontruth-functionally compound statements
• A nontruth-functionally compound statement is a
  compound statement whose truth or falsehood is
  independent of the truth-values (truth or
  falsehood) of its component statement.
• Example It is my opinion that this course is
  easy is compound. It contains the statement
  This course is easy. The statement describes
  the speaker. The truth or falsehood of the
  statement is independent of its component
  proposition.
• Example John believes that Juanita likes
  opera is true or false regardless of Juanitas
  musical tastes.

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Compound Statements (pp. 202-207)

• Truth-functionally compound statements
• The truth value of a truth-functionally compound
  statement is wholly dependent upon the truth
  values of its component statements.
• There is a symbolic apparatus that has been
  developed to accompany truth-functionally
  compound statements. The symbolic
  representations are included here, as they are in
  the book.

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Compound Statements (pp. 202-207)

• Types of truth-functionally compound statements
• Negation not, it is not the case that, no (p)
• The negation of a true statement is a false
  statement. The negation of a false statement is
  a true statement.
• Conjunction, conjuncts and, yet, but, although,
  however, nevertheless, even though (p q)
• A conjunction is true if and only if both of its
  conjuncts are true.

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Compound Statements (pp. 202-207)

• Disjunction, disjuncts or, either or ,
  unless (p v q)
• A disjunction is true except when both of its
  disjuncts are false.
• Conditionals, antecedents and consequents if
  then , only if , provided that, on the
  condition that (p ? q)
• The if-clause of a conditional is the antecedent
  the then-clause if the consequent.
• A conditional is true except when its antecedent
  is true and its consequent is false.

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Compound Statements (pp. 202-207)

• Biconditionals if and only if , just in
  case that (p ? q)
• A biconditional is true if and only if the
  statements the statements flanking the if and
  only if have the same truth value both true or
  both false.
• Grouping Indicators
• Commas and semicolons group in English
  parentheses, square brackets ( ), and braces (
  ) group in symbolese.

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Compound Statements (pp. 202-207)

• Determining truth values of compound statements
• In determining the truth value of a complex
  statement, you begin with statements most deeply
  embedded in the complex statement. You work out
  the truth value of the whole by working out the
  truth values of the proper parts.

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Compound Statements Examples of Determining
Truth Values

• George W. Bush was president in 2002 and Texas is
  in the United States.
• Both component statements (conjuncts) are true.
  So the whole statement the conjunction is
  true.
• Either Richmond is in Virginia or Richmond is in
  Norway.
• The first disjunct is true, so the whole
  statement is true.
• If Honolulu is in Hawaii, then George W. Bush was
  elected president in 1832.
• The antecedent is true. The consequent is false.
  So the statement is false.

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Compound Statements Examples of Determining
Truth Values

• If the moon is made of apple pie, then Rush
  Limbaugh talks on the radio.
• The antecedent is false, so the statement is
  true.
• Also, the consequent is true, so the statement is
  true.
• If the moon is not made of apple pie, then Cedar
  Rapids is in Iowa.
• The statement, The moon is made of apple pie is
  false, so its denial is true.
• The antecedent is true and the consequent is
  true. So, the statement is true.

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Compound Statements Examples of Determining
Truth Values

• If Miami is in Florida, then the South won the
  Civil War and either Washington, D.C. is the
  home of the Chicago Cubs or Green Bay is the home
  of the Packers.
• The first conjunct the conditional is false,
  since its antecedent is true and its consequent
  is false.
• The second conjunct is true, since the second
  disjunct is true, even though the first disjunct
  is false.
• Since the compound statement is a conjunction and
  one of its conjuncts is false, the entire
  statement is false.
• Since the first conjunct was false, it wouldnt
  have been necessary to examine the truth value of
  the second conjunct.

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Compound Statements Examples of Determining
Truth Values

• Yale is in Connecticut if and only if the
  University of Hawaii is in North Dakota or
  motley moose munch mice meditatively only if
  George W. Bush was president in 2002.
• The first disjunct the biconditional is
  false, since it is true that Yale is in
  Connecticut and its false that the University of
  Hawaii is in North Dakota.
• The second disjunct could be restated as, If
  motley moose munch mice meditatively, then George
  W. Bush was president in 2002. You probably
  dont know a lot about the personal habits of
  motley moose although I would question the
  truth of the antecedent. If its false, the
  conditional is true. But the consequent is true,
  so regardless of the truth value of the
  antecedent, the conditional is true. So, the
  second disjunct is true.
• Since at least one of the disjuncts is true, the
  disjunctive statement is true.