Logical Connectives

Transcript

2. “Our life is frittered away by detail. Simplify, simplify.” Henry David Thoreau
3. Logical Connectives Demystifying the symbols ¬, ∧, ∨ and ⊕ Ifeanyi Oraelosi - Trainer, Andela
4. Logical Negation ”NOT”
5. 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”
6. Logical Negation Truth table Venn Diagram p ¬p F T T F p ¬p
7. Logical Conjunction “AND”
8. 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”
9. 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
10. Logical Inclusive Disjunction ”OR”
11. 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”
12. 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
13. Logical Exclusive Disjunction ?
14. 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.
15. 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
16. Exhale.
17. 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
18. “If you don't know where you are going any road can take you there.” Lewis Carroll