In 13-18 determine whether each sentence is a statement.Explain your answers. 19. a. Assuming that the following sentence is a statement,prove that 1+1 = 3:If this sentence is true, then 1+1 = 3.b. What can you deduce from part (a) about the status of"This sentence is true"? Why? (This example is knownas Löb's paradox.)

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Answered: In 13-18 determine whether each…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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09:22 Question 3 3. [30] Write each of these propositions by using propositional variables and the logical connectives. a) For you to win the contest it is necessary and sufficient that you have the only winning ticket. b) It is necessary to walk eight miles to get to the top of Long's Peak.
9. Given the statement : The sum of two odd integers is even. (a) Express it as an implication.
Question 4 Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model: SALES-a+BAGE+YMIL+SENG Where SALES= amount that a vehicle is sold for($000's), AGE = age of the vehicle, MIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: The regression equation is ***** Predictor Coef StDev t-ratio p-value Constant 1.7586 0.2525 6.9648 0.0000 AGE 0.2124 0.3175 0.5042 -2.0991 7.7664 MIL -0.7527 0.3586 大* ENG 4.8124 0.6196 0.0000 Analysis of Variance Source I p DF SS MS Regression 413.1291 138.7097 ** * 0.00 Error 50 457.7607 2.2888 Total 53
9. Tommy Flanagan was telling you what he ate yesterday afternoon. He tells you, “I had either popcom or raisins. Also, if I had cucumber sandwiches, then I had soda. But I didn't drink soda or tea." Of course you know that Tommy is the world's worst liar, and everything he says is false. What did Tommy eat? Justify your answer by writing all of Tommy's statements using sentence variables (P,Q.R,S,T), taking their negations, and using these to deduce what Tommy actually ate. [8]
What is the hypothesis in a conditional statement, "If I had wings, I could fly"?
17. Each of the following sentences expresses an implica- tion. Rewrite each in the form "If p, then q." (a) Touch those cookies if you want a spanking. (b) Touch those cookies and you'll be sorry. (c) You leave or I'll set the dog on you. (d) I will if you will. (e) I will go unless you stop that.
20.
7. Say we are given that the statement p A (p → q) is true. Can we deduce the statement q?
m2.1 -4
2. The truth table for conditional (“if...then...") can be quite confusing. Here it is. T T F F F T F F T Consider the example “For every integer n, if n>2 then n²> 4." In this case p represents "n> 2" and q represents "n²> 4." Thus if n =3 then p is true and q is true. (a) Find another value of n that makes p true and q true. (b) Find a value for n that makes p false and q false. (c) Find a value for n that makes p false and q true. (d) Find a value for n that make p true and q false. Explain any problems you have. Why are you having these problems?
Example 18 Which of the following is the converse of the statement? "If Billu secure good marks, then he will get a bicycle." (A) If Billu will not get bicycle, then he will not secure good mar (B) If Billu will get a bicycle, then he will secure good marke (C) If Billu will get a bicycle, then he will not secure good marks. (D) If Billu will not get a bicycle, then he will secure good marks.
1.

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