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Logical Connectives
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Ifeanyi Oraelosi
April 19, 2015
Science
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33
Logical Connectives
Ifeanyi Oraelosi
April 19, 2015
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Transcript
None
“Our life is frittered away by detail. Simplify, simplify.” Henry
David Thoreau
Logical Connectives Demystifying the symbols ¬, ∧, ∨ and ⊕
Ifeanyi Oraelosi - Trainer, Andela
Logical Negation ”NOT”
Logical Negation - Unary operator ¬ - Converts a proposition
p to another proposition ¬p such that ¬p is false when p is true and vice versa. - “not p”
Logical Negation Truth table Venn Diagram p ¬p F T
T F p ¬p
Logical Conjunction “AND”
Logical Conjunction - Binary operator ∧ - Combines two propositions
p and q to create a compound proposition p ∧ q such that p ∧ q is true only when p is true and q is true. - “p and q”
Logical Conjunction Truth table Venn Diagram p q p ∧
q F F F F T F T F F T T T p p p ∧ q q
Logical Inclusive Disjunction ”OR”
Logical Inclusive Disjunction - Binary operator ∨ - Combines two
propositions p and q to create a compound proposition p ∨ q such that p ∨ q is false only when p is false and q is false. - “p or q”
Logical Inclusive Disjunction Truth table Venn Diagram p q p
∨ q F F F F T T T F T T T T p p ∨ q
Logical Exclusive Disjunction ?
Logical Exclusive Disjunction - Binary operator ⊕ - Combines two
propositions p and q to create a compound proposition p ⊕ q such that p ⊕ q is false when both p and q are true or when both p and q are false.
Logical Exclusive Disjunction Truth table Venn Diagram p q p
⊕ q F F F F T T T F T T T F p p ⊕ q p ⊕ q
Exhale.
Activity. The Art of Translation Let p be the proposition
“This meetup will end by exactly 5pm” and q be the proposition “Propositional logic is too abstract”. Let’s express the following as natural English sentences: - ¬ p - ¬ q - p ∧ q - p ∨ q - ¬ p ∨ q - ¬ q ∨ ¬ p
“If you don't know where you are going any road
can take you there.” Lewis Carroll