Math Logic Flashcards

1
Q

a statement that may be true or false

A

proposition

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1
Q

Enumerate the 5 connectives of compound propositions

A
  1. Negation
  2. Conjunction
  3. Disjunction
  4. Implication
  5. Biconditional
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2
Q

3 kinds of implication

A
  1. Converse
  2. Inverse
  3. Contrapositive
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3
Q

switching of orders ng proposition; q –> p

A

Converse

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3
Q

negation of proposition; ~q –> ~p

A

inverse

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3
Q

switching of orders and negation ng proposition; ~q –> ~p

A

contrapositive

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3
Q

3 terms under logical equivalence

A
  1. tautology
  2. contradiction
  3. contingency
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4
Q

proposition that is always true

A

tautology

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5
Q

proposition that is always false

A

contradiction

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6
Q

neither tautology nor contradiction

A

contingency

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7
Q

assumption; where we draw our conclusions

A

premises

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8
Q

templates to construct valid argument

A

rules of inference

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9
Q

result of assumptions

A

conclusion

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10
Q

set of premises with one conclusion

A

argument

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11
Q

8 types of inference rules

A
  1. Modus ponens
  2. Modus tollens
  3. Hypothetical syllogism
  4. Disjunctive syllogism
  5. Addition
  6. Simplification
  7. Conjunction
  8. Resolution
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12
Q

if p then q
p
therefore q

A

Modus ponens

13
Q

if p then q
not q
therefore not p

A

Modus tollens

14
Q
  • if p then q
  • if q then r
    therefore if p then r
A

Hypothetical syllogism

15
Q
  • p or q
  • not p
  • therefore q
A

Disjunctive syllogism

16
Q
  • p

- therefore p or q

A

Addition

17
Q

p and q
therefore q

or

therefore q

A

Simplification

18
Q

p
q
therefore p and q

A

Conjunction

19
Q

p or q
not p or r
therefore q or r

A

Resolution

20
Q

10 logical equivalences

A
  1. Identity laws
  2. Domination laws
  3. Indempotent laws
  4. Double negation laws
  5. Absorbtion laws
  6. Negation laws
  7. Commutative laws
  8. Associative laws
  9. Distributive laws
  10. De morgan’s laws