In each  represent the common form of each argument using letters to stand for component sentences, and fill in the blanks so that the argument in part (b) has the same logical form as the argument in part (a). a. If all computer programs contain errors, then this program contains an error.This program does not contain an error.Therefore, it is not the case that all computer programs contain errors.b. If _______________, then _____________.2 is not odd.Therefore, it is not the case that all prime numbers are odd.

Justify each conclusion with a derivation rule. (a) If Joe is artistic, he must also be creative. Joe is not creative. Therefore, Joe is not artistic. O De Morgan's Laws O double negation O modus ponens O modus tollens O simplification (b) Lingli is both athletic and intelligent. Therefore, Lingli is athletic. O De Morgan's Laws O double negation O modus ponens O modus tollens O simplification (c) If Monique is 18 years old, then she may vote. Monique is 18 years old. Therefore, Monique may vote. O De Morgan's Laws O double negation O modus ponens O modus tollens O simplification (d) Marianne has never been north of Saskatoon or south of Santo Domingo. In other words, she has never been north of Saskatoon and she has never been south of Santo Domingo. O De Morgan's Laws O double negation O modus ponens O modus tollens O simplification

a. Make a truth table for p -a (the inverse of p → q). Your first two columns should be the same as the first two columns of the table for p - q. The last columns of the two tables should be different. Are they? Is ~p → ~q logically equivalent to p q? b. Compare the truth table for ~p - ~g (the inverse of p - q) with the truth table for g-p (the converse of p - g). Are the last columns the same? Are the inverse and the converse logically equivalent?

ii. Let F(x,y) be the open sentence "x can fool y" where the domain of discourse is the set of all people in the world. Express each of these statements using logical quantifiers. c. Everybody can fool somebody. e. Everyone can be fooled by somebody. f. There is somebody who can be fooled by everybody.