9. All pesticides are harmful to the environment. No fertilizer is a pesticide. Therefore, no fertilizer is harmful to the environment. 10. Some professors wear glasses. Mr. Einstein wears glasses. Therefore, Mr. Einstein is a professor.

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?

Determine whether the argument is valid or invalid. No A are B, all B are C, and no C are D. Thus, no A are D. This argument is because

Are the following expressions logically equivalent? (present a truthtable)~p ⋁ ~q ⋁ ~ r ; ~ (p ⋀ r ⋀ q)

(a) Prove by using logical arguments (not by sketching Venn diagrams) that (AUB) = Aªn Bª.

Construct a Venn diagram to determine the validity of the given argument. 1. ??? ?????? ??? ??????? ____ _2. ???? ?? ?? ??????_____ ?ℎ???????, ???? ?? ? ?????

Question 12 Determine whether the following symbolized argument is valid or invalid by identifying the form of each. In some cases the argument must be rewritten using double negation or commutativity before it has a named form. Argument without an identifiable form is invalid. KOR EOR KJE a) CD-invalid. b) HS-valid. c) CD-valid. d) Invalid.

Construct a Venn diagram to determine the validity of the given argument. No vegetarians eat meat. All vegans are vegetarians.   Therefore, no vegans eat meat.

Answer the following question:a) What is an argument?