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SECOND TERM
DISCRETE STRUCTURES
LOGIC
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Cards (60)
These are letters to denote propositions.
Propositional Variables
Between true (T) or false (F), what is the equivalent of 1?
True
Between true (T) or false (F), what is the equivalent of 0?
False
This is a declarative sentence that is either TRUE or FALSE.
Proposition
What is NOT true about Propositions?
a.) It is not both TRUE and FALSE at the same time.
b.) It can be both TRUE and FALSE at the same time.
c.) It is not neither TRUE nor FALSE.
d.) It is not 50% TRUE and 50% FALSE.
B.
These are used to form compound propositions.
Operators
What operator does the symbols ~ or ¬ refer to?
Negation
What operator does the symbol ∧ refer to?
Conjunction
What operator does the symbol ∨ refer to?
Disjunction
What operator does the symbol ⊕ refer to?
Exlusive-OR
It indicates the opposite of the statement --- "It is not the case that..."
Negation
It is a compound statement formed by the word AND to join two simple propositions.
Conjunction
It is a compound statement formed by the word OR to join two simple propositions.
Disjunction
It refers to a logical operation exclusive disjunction.
Exclusive-OR
What operator does the symbol ⇒ or → refer to?
Conditional / Implication
What operator does the symbol ⇐⇒ refer to?
Biconditional
T | F
F | T
Negation
T | T | T
T | F | F
F | T | F
F | F | F
Conjunction
T | T | T
T | F | T
F | T | T
F | F | F
Disjunction
T | T | F
T | F | T
F | T | T
F | F | F
Exclusive-OR
T | T | T
T | F | F
F | T | T
F | F | T
Conditional / Implication
T | T | T
T | F | F
F | T | F
F | F | T
Biconditional
This refers to combination of one or more propositions using logical connectives or operators.
Compound Propositions
Between p and q, the hypothesis _ is also called the sufficient condition, premise, or antecedent.
p
Between p and q, the hypothesis _ is also called the necessary condition or the consequence.
q
This means always TRUE logical expression.
Tautology
This means always FALSE logical expression.
Contradiction / Fallacy
This means the logical expression is neither true or false.
Contingency
p → q
Given / Direct
~q → ~p
Contrapositive
~p → ~q
Inverse
q → p
Converse
What law does the following logical equivalence refer to?
p v F ≡ p
p ∧ T ≡ p
Identity
What law does the following logical equivalence refer to?
p ∨ T ≡ T
p ∧ F ≡ F
Domination
What law does the following logical equivalence refer to?
p ∨ p ≡ p
p ∧ p ≡ p
Idempotent
What law does the following logical equivalence refer to?
~(~p) ≡ p
Double Negation
What law does the following logical equivalence refer to?
p ∨ q ≡ q ∨ p
p ∧ q ≡ q ∧ p
Commutative
What law does the following logical equivalence refer to?
(p ∨ q) ∨ r ≡ p ∨ (q ∨ r)
(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)
Associative
What law does the following logical equivalence refer to?
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
Distributive
What law does the following logical equivalence refer to?
~(p ∨ q) ≡ ~p ∧ ~q
~(p ∧ q) ≡ ~p ∨ ~q
De Morgan's
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