For the argument below, perform the following a) Translate the argument into symbolic form. b) Use a truth table to determine whether the argument is valid or invalid. (Ignore differences in past, present, and future tense.) My clothes are too small and I need new clothes. If I need new clothes, then I'll go buy some new clothes. \therefore If I buy some new clothes, then my clothes are too small a) Let $p$ be \"My clothes are too small,\" let $q$ be \"I need new clothes,\" and let $r$ be \"I'll go buy some new clothes.\" What is the argument in symbolic form? A. $p \rightarrow q$ $q \rightarrow r$ $\therefore r \rightarrow p$ B. $p \rightarrow q$ $q \rightarrow r$ $\therefore p \rightarrow r$ C. $p \land q$ $q \rightarrow r$ $\therefore r \rightarrow p$ D. $p \land q$ $q \rightarrow r$ $\therefore r \rightarrow p$ b) Is the given argument valid or invalid? A. The argument is valid because the truth table indicates the conditional statement to be a tautology
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Whenever an argument is valid a. it has a true conclusion. b. it has true premises and a true conclusion. c. it has true premises if it has a true conclusion. d. it has a true conclusion if all of its premises are true. e. it is sound. f. it is sound if all its premises are true. g. it has a true conclusion if it is sound. h. it has a false conclusion if it has a false premise. i. it either has a true conclusion or has at least one false premise. j. it does not have all true premises with a false conclusion. k. it has consistent premises. Every invalid argument a. has a false conclusion if all its premises are true. b. has true premises and a false conclusion, c. has inconsistent premises. d. has a false conclusion. e. is unsound. f. has consistent premises.
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Determine whether the following statement is always true. If it is not, provide a counterexample.
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