Discussion2_text

Discussion2_text - people A and B Determine if possible...

This preview shows pages 1–2. Sign up to view the full content.

ECS20 Discussion 2 Week 2: April 4-8, 2016 Exercise 1 Let p and q be two statements. a) Write down the truth tables for ( p q ) q and ( p q ) q . What do you notice about the truth tables? Based on this result, a creative student concludes that you can always interchange the symbol “and” and “or” without changing the truth table. Is the student right? b) Write down the truth tables for ( p q ) p and ( p q ) p . What do you think of the rule formulated by the students in (a)? Exercise 2 Let p, q, and r be three propositions. Prove or disprove the following statements using truth tables: a) p  p q r is equivalent to q r b) p  p q r is equivalent to q r Can you find a simpler way to prove the same properties? Exercise 3 Construct a truth table for the compound propositions: a) p  q b) p  q Exercise 4 This exercise relate to the inhabitants of the island of knights and knaves created by Smullyan, where knights always tell the truth and knaves always lie. You encounter two

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: people, A and B. Determine, if possible, what A and B are if they address you in the way described. If you cannot determine what these two people are, can you draw any conclusions? a) A says “At least one of us is a knave” and B says nothing. b) A says “We are both knaves” and B says nothing. Exercise 4 This exercise relates again to the inhabitants of the island created by Smullyan, except that this time there are three types of inhabitants, knights that always tell the truth, knaves that always lie, and spies that may tell the truth of lie. You encounter three people, A, B, and C and you know that one is a knight, one is a knave, and one is a spy. Determine, if possible, what A, B, and C are if they address you in the way described. If you cannot determine what these three people are, can you draw any conclusions? PA: A says ``C is a knave" PB: B says ``A is the knight" PC: C says ``I am the spy"...
View Full Document

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern