A1257278166TUiOH

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MGF1106
Unit One Ex. 2.7 Venn Diagrams and Valid
Arguments Objectives 36-37
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Ex. 2.7
Objective 36
To classify a reasoning process as deductive or
inductive
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There are two kinds of reasoning processes,
___________ and _____________.
inductive
deductive
Inductive reasoning
_____________________ is reasoning in which the
reasoning goes from specific situations to
generalizations.
Deductive reasoning
____________________ is reasoning in which the
reasoning goes from generalizations to specific
situations.
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Classify each reasoning process as deductive or
inductive.
1) Last Tuesday we had chicken for
dinner. This Tuesday we had chicken for
dinner._____________________ ?Next Tuesday
we will have chicken for dinner.
inductive
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2) All boys like baseball. Timmy is a boy._____
?Timmy likes baseball.
deductive
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Ex. 2.7
Objective 37
To use a Venn diagram to determine the validity
of an argument
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An assumption, law, rule, widely held idea, or an
observation.
premise
The result of reasoning, either inductively or
deductively.
conclusion
Made up of the premises and conclusion.
argument
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An argument may be valid or invalid.
valid
A _________ argument is one in which the
conclusion necessarily follows from the premises.
When the conclusion does not necessarily follow
from a set of premises, we say the argument is
__________.
invalid
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Venn diagrams
The use of __________________is one method of
determining whether an argument is valid or
invalid.
A Venn diagram for statements in the form All
ps are qs. is shown below.
Draw a circle for q
q
Draw a circle for p entirely in q.
p
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A Venn diagram for No ps are qs. is shown
below
Draw a circle for q
q
p
Draw a circle for p that has no elements in
common with q.
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A Venn diagram for the statement in the form of
Some ps are qs. is shown below.
Draw a circle for q
q
p
x
Draw a circle for p that intersects q
X represents the common elements.
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Use a Venn diagram to determine the validity of
the given argument.
1) All cats are animals. Misty is a cat.______
?Misty is an animal.
valid
Misty
cats
animals
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2) No girls like baseball. Sue likes
baseball.___ ?Sue is not a girl.
valid
baseball
girls
Sue
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3) Some teachers are happy. Mrs. Jones is a
teacher.____ ?Mrs. Jones is happy.
invalid
teachers
happy
x
Let x represent Mrs. Jones.
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4) Some mothers play golf. All people who play
golf are happy. ?Some mothers are happy.
valid
x
golf
mothers
happy
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5) All athletes are strong. All strong people
lift weights. All people who lift weights have
muscles.____________________ ?All athletes
have muscles.
valid
athletes
strong
weights
muscles