Truth Tables

Monday, 25 March 2019

6:17 PM

A child declares that "today is opposites day!" - a day when all statements have the opposite Of their intended meaning. The teacher responds by saying that "today is not opposites day!". Based on this information, is today really opposites day? a) Fill in the table below with T for true statements and F for false statements. when it is opposites day Saying "today is opposites day!" Saying "today is not opposites day!" when it is not opposites day T Gap 1 Submit part Your answer is correct. You were awarded 1 mark. Gap 2

 

Gap 2 Your answer is correct. You were awarded 1 mark. Gap 3 Your answer is correct. You were awarded 1 mark. Gap 4 Your answer is correct. You were awarded 1 mark. You scored 4 marks for this part. Score: 4/4 Answered

 

b) Both statements "Today is opposites day" and "Today is not opposites day" give no information about whether today is, or is not, actually opposites day because El "Today is opposites day" is always false. "Today is opposites day" is always true. Z] "Today is not opposites day" is always true. "Today is not opposites day" is always false. Submit part

 

Enter T if true, else enter F. Complete the following truth table: P q P-*æq

 

In classical logic the proposition "1f p then q" is represented by the notatoin p q. This is only false when p is true and q is false. a) Fill in the following truth table A NCI) T F F T F Show steps (Your score will not be affected.)

 

b) Using your truth table above, which ofthe following is logically equivalent top —+ q? Oæ(pAq) ON(pvæq) A Submit part A æq) is correct. You were awarded 1 mark. You scored 1 mark for this part. Score: 1/1 Answered

 

c) Using De Morgans laws we can rewrite the correct answer to part (b) as: O A q @ q O rop V æq

 

Fill in the following logic table. Use T for true and F for false. Show steps P (Your score will not be affected.) q pVq

 

Consider the following quote from Catch-22, a 1961 satirical novel by Joseph Heller. The famous passage below describes how a pilot could only be excused from flying dangerous missions if they requested an evaluation, in which they were shown to be insane. However, there was a catch (catch-22): anybody who wanted to get out combat duty isn't crazy. There was only one catch and that was Catch-22, which specified that a concern for one's safety in the face ofdangers that were real and immediate was the process Of a rational mind. Orr was crazy and could be grounded. All he had to do was ask; and as soon as he did, he would no longer be crazy and would have to fly more missions. Orr would be crazy to fly more missions and sane if he didn't, but ifhe were sane he had to fly them. If he flew them he was crazy and didn't have to, but if he didn 't want to he was sane and had to. Yossarian was moved very deeply by the absolute simplicity of this clause of Catch-22 and let out a respectful whistle. (p. 56, ch. 5) Let E be the proposition "The pilot was excused from flying combat missions", I be the proposition "the pilot is insane" and R be the proposition "the pilot requested an evalutaion". The following true table might be hepful below.

 

Machine generated alternative text:

 

Machine generated alternative text: a) Let PI be the proposition "If a pilot has been excused from flying then she/he has requested an evaluation and is insane". PI can be expressed as: e E + (1 AR) A (O v R) O Ev (1 AR) OE (1 A R) Submit part You chose a correct answer. You were awarded 1 mark. You scored 1 mark for this part. Score: 1/1 Answered

 

Machine generated alternative text: b) Let P2 be the proposition "An insane person doesn't request an evaluation". P2 can be expressed as: or. 1 e R o IAR Submit part You chose a correct answer. You were awarded 1 mark. You scored 1 mark for this part. Score: 1/1 Answered

 

Machine generated alternative text: c) For which rows in the truth table above are the both proposition PI and P2 true? Row 1 2 Row 3 Row4 D Row5 D Row 6 Row 7 Row 8 Submit part Row 1 is a correct choice. You were awarded 0.67 marks. Row 2 is a correct choice. You were awarded 0.67 marks. Row 3 is a correct choice. You were awarded 0.66 marks. You scored 2 marks for this part. Score: 2/2 Answered

 

Machine generated alternative text: d) In the rows where propositions PI and P2 are true, what else is always true? C] E - The pilot was excused from flying combat missions C] I- The pilot is insane C] R- The pilot requested an evalutaion Z] euE - The pilot was not excused from flying combat missions C] 001- The pilot is sane C] - The pilot did not request an evalutaion Submit part Correct, no one is excused from flying. You were awarded 2 marks. You scored 2 marks for this part. Score: 2/2 Answered

 

 

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