Activity

Which of the following are propositions?1. The sky is blue.2. 2+2 = 3.3. No smoking.What is the negation of each of these propositions?4. Today is Monday.5. 2+2

p is “It is below freezing”q is “It is snowing”Express each of the following as English sentences.6. p ^ q7. p ^ q8. p q9. p v qWrite these propositions using p and q and logicalconnectives.10. It is not snowing.11. If it is not below freezing then it is not snowing.12. It is snowing if and only if it is below freezing.1/12/2010 Chapter 1.1 and 1.2

Which of the following conditionals are true.13. If 2+3=5 then 1+1=214. If 2+2=5 then 1+1=315. If 2+3=5 then 1+1=3State the converse, inverse and contrapositive16. If it snows today then I will ski tomorrow.17. Construct a truth table for: p ^ (qr)18. Find the bitwise OR and AND of:1001 1001^ 1110 v 11101/12/2010 Chapter 1.1 and 1.2

19. Use truth tables to verify: (p v q) p ^ qP(x) is x4. What are the truth values of:20. P(0)21. P(4)22. P(6)C(x) is “x is a comedian”The domain is all people.F(x) is “x is funny”Translate:23. x(C(x) F(x))24. x(C(x) F(x))1/12/2010 Chapter 1.1 and 1.2

Determine the truth value of each if the domainconsists of all integers.25. n(n 2 > n)26. n(n 2 < 0 )27. n(n 2 > n)28. n(n 2 < 0 )1/12/2010 Chapter 1.1 and 1.2

Which of the following are propositions?1. The sky is blue. Yes2. 2+2 = 3. Yes3. No smoking. NoWhat is the negation of each of these propositions?4. Today is Monday. Today is not Monday.5. 2+2

p is “It is below freezing”q is “It is snowing”Express each of the following as English sentences.6. It is below freezing and snowing. p ^ q7. It is not below freezing and it is not snowing. p ^ q8. If it is below freezing then it is snowing. p q9. It is snowing or below freezing. p v qWrite these propositions using p and q and logicalconnectives.10. It is not snowing. q11. If it is not below freezing then it is not snowing.pq12. It is snowing if and only if it is below freezing. pq1/12/2010 Chapter 1.1 and 1.2

Which of the following conditionals are true.13. If 2+3=5 then 1+1=2 True14. If 2+2=5 then 1+1=3 True15. If 2+3=5 then 1+1=3 FalseState the converse, inverse and contrapositive16. If it snows today then I will ski tomorrow.Converse: If I will ski tomorrow then it snows today.Inverse: If it does not snow today then I will not skitomorrow.Contrapositive: If I do not ski tomorrow then it did notsnow today.1/12/2010 Chapter 1.1 and 1.2

17. Construct a truth table for: p ^ (qr)p q r p qr p ^(qr)T T T F T FT T F F F FT F T F T FT F F F T FF T T T T TF T F T F FF F T T T TF F F T T T18. Find the bitwise OR and AND of:1001 1001^ 1110 v 11101000 11111/12/2010 Chapter 1.1 and 1.2

19. Use truth tables to verify: (p v q) p ^ qp q p q p v q (p vq) p ^ qT T F F T F FT F F T T F FF T T F T F FF F T T F T TP(x) is x4. What are the truth values of:20. P(0) True21. P(4) True22. P(6) FalseC(x) is “x is a comedian” F(x) is “x is funny”The domain is all people.Translate:24. x(C(x) F(x)) For all people, if they are acomedian then they are funny.25. x(C(x) F(x)) There exists a person that if theyare a comedian then they are funny.1/12/2010 Chapter 1.1 and 1.2

Determine the truth value of each if the domainconsists of all integers.25. n(n 2 > n) False, 1 2 > 126. n(n 2 < 0 ) False, n 2 027. n(n 2 > n)=n(n 2 > n)=n(n 2 n) True, 1 2 128. n(n 2 < 0 )=n(n 2 < 0 )=n(n 2 0) True1/12/2010 Chapter 1.1 and 1.2