LOGIC:

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LOGIC

• SYLLOGISMS

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Syllogism A set of statements called premises,
which lead to one logical conclusion.
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If the premises are true, (and we assume they
are), then the conclusion must be true.
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(Note This symbol means Therefore.
It signals the conclusion.)
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Law of Syllogism
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• If a figure is a rectangle, then it is a
  parallelogram.
• If a figure is a parallelogram, then its
  diagonals bisect each other.
• __________________________

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• If a figure is a rectangle, then it is a
  parallelogram.
• If a figure is a parallelogram, then its
  diagonals bisect each other.
• __________________________

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• If a figure is a rectangle, then it is a
  parallelogram.
• If a figure is a parallelogram, then its
  diagonals bisect each other.
• __________________________

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• If a figure is a rectangle, then it is a
  parallelogram.
• If a figure is a parallelogram, then its
  diagonals bisect.
• __________________________

If a figure is a rectangle, then its diagonals
bisect.
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Law of Detachment
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• If a figure is a rectangle, then it is a
  parallelogram.
• ABCD is a rectangle.
• __________________________

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• If a figure is a rectangle, then it is a
  parallelogram.
• ABCD is a rectangle.
• __________________________

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• If a figure is a rectangle, then it is a
  parallelogram.
• ABCD is a rectangle.
• __________________________

ABCD is a parallelogram.
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Law of Contrapositive
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• If a figure is a rectangle, then it is a
  parallelogram.
• ABCD is not a parallelogram.
• __________________________

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• If a figure is a rectangle, then it is a
  parallelogram.
• ABCD is not a parallelogram.
• __________________________

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• If a figure is a rectangle, then it is a
  parallelogram.
• ABCD is not a parallelogram.
• __________________________

ABCD is not a rectangle.
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Time to Practice
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In the following examples, use the given law of
syllogism to draw the correct conclusion from the
set of premises.
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1. If frogs fly then toads talk. Frogs
fly. -----------------------------
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Law of Detachment
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1. If frogs fly then toads talk. Frogs
fly. -----------------------------
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1. If frogs fly then toads talk. Frogs
fly. ----------------------------- Toads
talk.
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2. If hens heckle then crows dont care. Crows
care. -----------------------
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Law of Contrapositive
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2. If hens heckle then crows dont care. Crows
care. -----------------------
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2. If hens heckle then crows dont care. Crows
care. ----------------------- Hens dont
heckle.
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3. If ants dont ask then flies dont fret. Ants
dont ask. ----------------------------
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Law of Detachment
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3. If ants dont ask then flies dont fret. Ants
dont ask. ----------------------------
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3. If ants dont ask then flies dont fret. Ants
dont ask. ---------------------------- Flies
dont fret.
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4. If Dave dives then Cal caves. If Cal caves
then Hank hikes. ---------------------------------
----
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Law of Syllogism
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4. If Dave dives then Cal caves. If Cal caves
then Hank hikes. ---------------------------------
----
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4. If Dave dives then Cal caves. If Cal caves
then Hank hikes. ---------------------------------
---- If Dave dives then Hank hikes.
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5. If dogs duel then rats wrestle. Rats dont
wrestle. -----------------------------
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Law of Contrapositive
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5. If dogs duel then rats wrestle. Rats dont
wrestle. -----------------------------
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5. If dogs duel then rats wrestle. Rats dont
wrestle. ----------------------------- Dogs
dont duel.
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Why does this one work?
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Here are the premises
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Replace with contrapositive
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Replace with contrapositive
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Use Law of Detatchment
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Law of Contrapositive