Do the following by answering all questions. 1. (argument forms) (a) Translate t

Question

Do the following by answering all questions. 1. (argument forms) (a) Translate the following into symbols: If I work all night on this homework, then I can answer all the exercises. If I answer all the exercises then I will understand the material. Therefore, if I work all night on this homework then I will understand the material. You need to specify what letters stand for each phrase and you should then write the argument given using and symbols only. (b) Do you recognize the argument form which Is shown in your symbols? (c) Set up which columns you will use to show that this argument is valid? Fill in your table with appropriate T's and F's. (d) By looking at the completed truth table, is this a valid argument? 2. (statements are logically equiovalent? There are 2 statements given in each of the 2 sections. Translate them into symbols, compare the truth tables for each of the 2 statements, and then say whether they are logically equivalent: (a) If r is a rational number, then r can be expressed as a then r can be expressed

Explanation / Answer

5:

Prime factrorization of 909,000 = 2^3 × 3^2 × 5^3 × 101

Prime factrorization of 1,111 = 11 × 101

6. Prime factrorization of 662 = 2 × 331

Prime factrorization of 414 = 2 × 3^2 × 23

hence common factor = 2

hence GCD(662, 414) = 2

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