Compound Proposition Compound Statements in Natural Language It's NOT raining outside Ne Zha AND Ao Bing both become good at the end of the film He is a football player OR a basketball player. IF 2+3=6,THEN n is a rational number. V3 is irrational IF AND ONLY IF Canada is located in Asia The truth of a compound The truths of all sub-propositions/statements proposition/statement depends on two factors The semantics of connectives
Compound Proposition Compound Statements in Natural Language It’s NOT raining outside Ne Zha AND Ao Bing both become good at the end of the film He is a football player OR a basketball player. IF 2+3=6, THEN 𝜋 is a rational number. √3 is irrational IF AND ONLY IF Canada is located in Asia The truth of a compound proposition/statement depends on two factors The truths of all sub-propositions/statements The semantics of connectives
Logic Connectives p T F F T Negation p All possible values of p “NOTp” p:It's raining outside p:It's NOT raining outside
Logic Connectives Negation ¬𝒑 “NOT p” 𝑝 ¬𝑝 T F F T All possible values of 𝑝 𝑝: It’s raining outside ¬𝑝: It’s NOT raining outside
Logic Connectives p pΛq T T T T F F F T F Conjunction F pΛq All possible values of <p,g p AND g" p:Ne Zha becomes good at the end of the film q:Ao Bing becomes good at the end of the film pAq:Both Ne Zha AND Ao Bing become good at the end of the film
Logic Connectives Conjunction 𝒑⋀𝒒 “𝒑 AND 𝒒” 𝑝 𝑞 𝑝⋀𝑞 T T T T F F F T F F F F All possible values of < 𝑝, 𝑞 > 𝑝: Ne Zha becomes good at the end of the film 𝑞: Ao Bing becomes good at the end of the film 𝑝⋀𝑞: Both Ne Zha AND Ao Bing become good at the end of the film
Logic Connectives p q pVq T T T T F T F T T Disjunction F F pVq All possible values of <p,g pORq” p:He is a football player. If the two propositions can not g:He is a basketball player.be true at the same time? pVq:He is a football player OR a basketball player
Logic Connectives Disjunction 𝒑⋁𝒒 “𝒑 OR 𝒒” 𝑝 𝑞 𝑝⋁𝑞 T T T T F T F T T F F F 𝑝: He is a football player. 𝑞: He is a basketball player. 𝑝⋁𝑞: He is a football player OR a basketball player. If the two propositions can not be true at the same time? All possible values of < 𝑝, 𝑞 >
Logic Connectives p q p⊕q T T F T F T Exclusive F T T E F Disjunction p⊕q All possible values of<p,g> p⊕g =(pVq∧(p∧q) “p XOR q” p⊕q=(p∧qV(p∧q) p:He is a football player. q:He is a basketball player. pq:He is a football player,otherwise he is a basketball player
Logic Connectives Exclusive Disjunction 𝒑 ⊕ 𝒒 “𝒑 XOR 𝒒” 𝑝 𝑞 𝑝 ⊕ 𝑞 T T F T F T F T T F F F 𝑝: He is a football player. 𝑞: He is a basketball player. 𝑝 ⊕ 𝑞: He is a football player, otherwise he is a basketball player. All possible values of < 𝑝, 𝑞 >