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LOGICAL DEDUCTION
Deduction and Syllogism
 Deduction is a process of reasoning
where we begin with a general truth
to a particular conclusion.
 Syllogism is the set of arguments
that derives a conclusion from two
previous statements called
“premises”.
Quantity of Arguments
 Quantity
Universal- signaled by the qualifiers all
and no.
All humans are mortal beings.
No male is female.
Particular- signaled by the qualifiers
some, few, most of, not all, ect.
Some birds can fly.
Not all mammals live on land.
Quality of Arguments
 Quality
Affirmative- consenting to something.
All humans are mortal beings.
Some birds can fly.
Negative- negating or denying
something
No male is female.
Not all mammals live on land.
Premises and Terms of
Syllogisms
Major Premise
 The first argument that contains the Middle
Term and Major Term.
 Major Term is the predicate of the Major Premise
and the Conclusion.
 Example:
All mortal beings will die.
All human beings are mortal beings.
Therefore, all human beings will die.
Major Term
Major Premise
Minor Premise
 The second argument that contains the Minor
Term and the Middle Term.
 Minor Term is the subject of the Minor Premise
and the Conclusion.
 Example:
All mortal beings will die.
All human beings are mortal beings.
Therefore, all human beings will die.
Minor Premise
Minor Term
Middle Term
 The subject of the Major Premise and the
predicate of the Minor premise.
 Example:
All mortal beings will die.
All human beings are mortal beings.
Therefore, all human beings will die.
Middle Term
Middle Term
RULES FOR DERIVING
CONCLUSIONS FROM TWO GIVEN
PREMISES
Rule 1
 The conclusion must not
contain the Middle Term.
 Example:
No male is female.
John is male.
Rule 2
 No term can be distributed in the
conclusion unless it is distributed in
the premises.
 Example:
All cats have fur.
Some furs are orange.
Therefore, some fur are
cats???
some cats are
Rule 3
 The middle term should he distributed
at least once in the premises.
Otherwise, the conclusion cannot
follow.
 Example:
All cats have fur.
Some furs are orange.
Therefore, some fur are
cats???
Rule 4
 No conclusion follows if both the
premises are particular.
Example:
Some that can fly are birds.
Some ducks can fly.
Therefore, some ducks are
birds.
Rule 5
No conclusion follows if both
the premises are negative.
Example:
No mango is bitter.
No balsam apple is mango.
Therefore, no apple is
bitter???
Rule 6
 No conclusion follows if the major
premise is particular and the
minor premise is negative.
Example:
Some dogs are bulls.
No tigers are dogs.
No dogs are tigers.???
Rule 7
If one premise is negative,
the conclusion must be
negative.
Example:
All grasses are
trees.
No tree is shrub.
Rule 8
If one premise is particular,
the conclusion must be
particular.
Example:
Some boys are thieves.
All thieves are bandits.
Some boys are bandits.
Rule 9
If both the premises are
affirmative, the conclusion
must be affirmative.
Example:
All women are
mothers.
All sisters are women
All sisters are mothers.
Rule 10
If both the premises are
universal, the conclusion must
be universal.
Examples:
All mortal beings will die.
All human beings are mortal
beings.
Therefore, all human beings will
die.
 All humans will die.
 ___________________________
 Lito will die.
 ___________________________
 All whales are mammals
 All whales have lungs.
 All animals are living beings.
 Some flying objects are animals.
 ___________________________
 Angles <90° are Acute Angles.
 Angle ABC is 40°.
 ___________________________
 ___________________________
 Beef is a red meat
 Beef contains iron.
 All birds have feathers.
 ___________________________
 Roosters have feathers.

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Logical deduction (With Activity)

  • 2. Deduction and Syllogism  Deduction is a process of reasoning where we begin with a general truth to a particular conclusion.  Syllogism is the set of arguments that derives a conclusion from two previous statements called “premises”.
  • 3. Quantity of Arguments  Quantity Universal- signaled by the qualifiers all and no. All humans are mortal beings. No male is female. Particular- signaled by the qualifiers some, few, most of, not all, ect. Some birds can fly. Not all mammals live on land.
  • 4. Quality of Arguments  Quality Affirmative- consenting to something. All humans are mortal beings. Some birds can fly. Negative- negating or denying something No male is female. Not all mammals live on land.
  • 5. Premises and Terms of Syllogisms
  • 6. Major Premise  The first argument that contains the Middle Term and Major Term.  Major Term is the predicate of the Major Premise and the Conclusion.  Example: All mortal beings will die. All human beings are mortal beings. Therefore, all human beings will die. Major Term Major Premise
  • 7. Minor Premise  The second argument that contains the Minor Term and the Middle Term.  Minor Term is the subject of the Minor Premise and the Conclusion.  Example: All mortal beings will die. All human beings are mortal beings. Therefore, all human beings will die. Minor Premise Minor Term
  • 8. Middle Term  The subject of the Major Premise and the predicate of the Minor premise.  Example: All mortal beings will die. All human beings are mortal beings. Therefore, all human beings will die. Middle Term Middle Term
  • 9. RULES FOR DERIVING CONCLUSIONS FROM TWO GIVEN PREMISES
  • 10. Rule 1  The conclusion must not contain the Middle Term.  Example: No male is female. John is male.
  • 11. Rule 2  No term can be distributed in the conclusion unless it is distributed in the premises.  Example: All cats have fur. Some furs are orange. Therefore, some fur are cats??? some cats are
  • 12. Rule 3  The middle term should he distributed at least once in the premises. Otherwise, the conclusion cannot follow.  Example: All cats have fur. Some furs are orange. Therefore, some fur are cats???
  • 13. Rule 4  No conclusion follows if both the premises are particular. Example: Some that can fly are birds. Some ducks can fly. Therefore, some ducks are birds.
  • 14. Rule 5 No conclusion follows if both the premises are negative. Example: No mango is bitter. No balsam apple is mango. Therefore, no apple is bitter???
  • 15. Rule 6  No conclusion follows if the major premise is particular and the minor premise is negative. Example: Some dogs are bulls. No tigers are dogs. No dogs are tigers.???
  • 16. Rule 7 If one premise is negative, the conclusion must be negative. Example: All grasses are trees. No tree is shrub.
  • 17. Rule 8 If one premise is particular, the conclusion must be particular. Example: Some boys are thieves. All thieves are bandits. Some boys are bandits.
  • 18. Rule 9 If both the premises are affirmative, the conclusion must be affirmative. Example: All women are mothers. All sisters are women All sisters are mothers.
  • 19. Rule 10 If both the premises are universal, the conclusion must be universal. Examples: All mortal beings will die. All human beings are mortal beings. Therefore, all human beings will die.
  • 20.  All humans will die.  ___________________________  Lito will die.
  • 21.  ___________________________  All whales are mammals  All whales have lungs.
  • 22.  All animals are living beings.  Some flying objects are animals.  ___________________________
  • 23.  Angles <90° are Acute Angles.  Angle ABC is 40°.  ___________________________
  • 24.  ___________________________  Beef is a red meat  Beef contains iron.
  • 25.  All birds have feathers.  ___________________________  Roosters have feathers.