Midterm 1 is early.IBefore drop date.IBefore most other midterms in CS.CS70: Lecture 2. Outline.1. Propositions.2. Propositional Forms.3. Implication Again.4. Wason’s Experiment5. Truth Tables6. QuantifiersPropositions: Statements that are true or false.√2 is irrational Proposition2+2 = 4Proposition2+2 = 3Proposition826th digit of pi is 4PropositionJohny Depp is a good actorNot a PropositionEvery even number > 2 is sum of 2 primesPropositionx + xNot a Proposition.4 + 5Not a Proposition.Propositions: Statements that are true or false.√2 is irrational Proposition2+2 = 4 Proposition2+2 = 3Proposition826th digit of pi is 4PropositionJohny Depp is a good actorNot a PropositionEvery even number > 2 is sum of 2 primesPropositionx + xNot a Proposition.4 + 5Not a Proposition.Propositions: Statements that are true or false.√2 is irrational Proposition2+2 = 4 Proposition2+2 = 3 Proposition826th digit of pi is 4PropositionJohny Depp is a good actorNot a PropositionEvery even number > 2 is sum of 2 primesPropositionx + xNot a Proposition.4 + 5Not a Proposition.Propositions: Statements that are true or false.√2 is irrational Proposition2+2 = 4 Proposition2+2 = 3 Proposition826th digit of pi is 4 PropositionJohny Depp is a good actorNot a PropositionEvery even number > 2 is sum of 2 primesPropositionx + xNot a Proposition.4 + 5Not a Proposition.Propositions: Statements that are true or false.√2 is irrational Proposition2+2 = 4 Proposition2+2 = 3 Proposition826th digit of pi is 4 PropositionJohny Depp is a good actor Not a PropositionEvery even number > 2 is sum of 2 primesPropositionx + xNot a Proposition.4 + 5Not a Proposition.Propositions: Statements that are true or false.√2 is irrational Proposition2+2 = 4 Proposition2+2 = 3 Proposition826th digit of pi is 4 PropositionJohny Depp is a good actor Not a PropositionEvery even number > 2 is sum of 2 primes Propositionx + x Not a Proposition.4 + 5Not a Proposition.Propositions: Statements that are true or false.√2 is irrational Proposition2+2 = 4 Proposition2+2 = 3 Proposition826th digit of pi is 4 PropositionJohny Depp is a good actor Not a PropositionEvery even number > 2 is sum of 2 primes Propositionx + x Not a Proposition.4 + 5 Not a Proposition.Propositional Forms.Conjunction: P ∧ QDisjunction: P ∨ QImplication: P =⇒ Q or ¬P ∨ Q“not (2 + 2 = 4)” – a new statement that is false...2 + 2 = 3 and 2 + 2 = 4 – a new statement that is falsePropositional Forms....IYou will do the homework or you will regret it.P ∨ QP = “You will do the homework.”Q = “You will regret it.”IMy name is Satish and I love math.P ∧ QP = “My name is Satish.”Q = “I love math.”Propositional Forms....IYou will do the homework or you will regret it.P ∨ QP = “You will do the homework.”Q = “You will regret it.”IMy name is Satish and I love math.P ∧ QP = “My name is Satish.”Q = “I love math.”Propositional Forms....IYou will do the homework or you will regret it.P ∨ QP = “You will do the homework.”Q = “You will regret it.”IMy name is Satish and I love math.P ∧ QP = “My name is Satish.”Q = “I love math.”Propositional Forms....IYou will do the homework or you will regret it.P ∨ QP = “You will do the homework.”Q = “You will regret it.”IMy name is Satish and I love math.P ∧ QP = “My name is Satish.”Q = “I love math.”Implication.P =⇒ Q interpreted as If P, then Q.If you stand in the rain, then you’ll get wet.P = “you stand in the rain”Q = “you will get wet”Only false if P is true and Q is false.Consequences:False implies anything. Anything implies true.If plant pollutes river, fish die.If fish die, plant p olluted river?Not necessarily.P =⇒ Q and Q = T does not mean P = TImplication.P =⇒ Q interpreted as If P, then Q.If you stand in the rain, then you’ll get wet.P = “you stand in the rain”Q = “you will get wet”Only false if P is true and Q is false.Consequences:False implies anything. Anything implies true.If plant pollutes river, fish die.If fish die, plant p olluted river?Not necessarily.P =⇒ Q and Q = T does not mean P = TImplication.P =⇒ Q interpreted as If P, then Q.If you stand in the rain, then you’ll get wet.P = “you stand in the rain”Q = “you will get wet”Only false if P is true and Q is false.Consequences:False implies anything. Anything implies true.If plant pollutes river, fish die.If fish die, plant p olluted river?Not necessarily.P =⇒ Q and Q = T does not mean P = TImplication.P =⇒ Q interpreted as If P, then Q.If you stand in the rain, then you’ll get wet.P = “you stand in the rain”Q = “you will get wet”Only false if P is true and Q is false.Consequences:False implies anything. Anything implies true.If plant pollutes river, fish die.If fish die, plant p olluted river?Not necessarily.P =⇒ Q and Q = T does not mean P = TImplication.P =⇒ Q interpreted as If P, then Q.If you stand in the rain, then you’ll get wet.P = “you stand in the rain”Q = “you will get wet”Only false if P is true and Q is false.Consequences:False implies anything. Anything implies true.If plant pollutes river, fish die.If fish die, plant p olluted river?Not necessarily.P =⇒ Q and Q = T does not mean P = TImplication.P =⇒ Q interpreted as If P, then Q.If you stand in the rain, then you’ll get wet.P = “you stand in the rain”Q = “you will get wet”Only false if P is true and Q is false.Consequences:False implies anything. Anything implies true.If plant pollutes river, fish die.If fish die, plant p olluted river?Not necessarily.P =⇒ Q and Q = T does not mean P = TImplication.P =⇒ Q interpreted as If P, then Q.If you stand in the rain, then you’ll get wet.P = “you stand in the rain”Q = “you will get wet”Only false if P is true and Q is false.Consequences:False implies anything. Anything implies true.If plant pollutes river, fish die.If fish die, plant p olluted river?Not necessarily.P =⇒ Q and Q = T does not mean P = TImplication and English.P =⇒ QIIf P, then Q.IQ if P.IP only if Q.IP is sufficient for Q.IQ is necessary for P.Implication and English.P =⇒ QIIf P, then Q.IQ if P.IP only if Q.IP is sufficient for Q.IQ is necessary for P.Implication and English.P =⇒ QIIf P, then Q.IQ if P.IP only if Q.IP is sufficient for Q.IQ is necessary for P.Wason’s experiment:1Suppose we have four cards on a table:I1st about Alice, 2nd about Bob, 3rd Charlie, 4th Donna.IOn side of each card is the
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