91Ó°ÊÓ

Express \(p \leftrightarrow q\) in terms of the Sheffer stroke. (Hint: \(p \leftrightarrow q \equiv\) \((p \rightarrow q) \wedge(q \rightarrow p) . )\) INote: Exercises \(57-64\) indicate that all boolean operators can be expressed in terms of the Sheffer strokell

Determine whether or not each is a contradiction. $$\sim p \leftrightarrow(p \vee \sim p)$$

Exercises \(65-78\) deal with propositions in fuzzy logic. Let \(p, q,\) and \(r\) be simple propositions with \(t(p)=1, t(q)=0.3,\) and \(t(r)=\) 0.5 . Compute the truth value of each, where \(s^{\prime}\) denotes the negation of the statement \(s\) . $$ \left(p^{\prime}\right)^{\prime} $$

Determine the truth value of each, where \(P(s)\) denotes an arbitrary predicate. $$(\forall x) \mathrm{P}(x) \rightarrow(\exists x) \mathrm{P}(x)$$

Let \(p, q,\) and \(r\) be simple propositions with \(t(p)=1, t(q)=0.3,\) and \(t(r)=\) \(0.5 .\) Compute the truth value of each, where \(s^{\prime}\) denotes the negation of the statement \(s\) $$p \wedge q$$

Determine the truth value of each, where \(\mathrm{P}(\mathrm{s})\) denotes an arbitrary predicate. $$(\forall x) P(x) \rightarrow(\exists x) P(x)$$

Exercises \(65-78\) deal with propositions in fuzzy logic. Let \(p, q,\) and \(r\) be simple propositions with \(t(p)=1, t(q)=0.3,\) and \(t(r)=\) 0.5 . Compute the truth value of each, where \(s^{\prime}\) denotes the negation of the statement \(s\) . $$ p \wedge q $$

Indicate the order in which each logical expression is evaluated by properly grouping the operands using parentheses. $$p \vee q \wedge r$$

Let \(p, q,\) and \(r\) be simple propositions with \(t(p)=1, t(q)=0.3,\) and \(t(r)=\) \(0.5 .\) Compute the truth value of each, where \(s^{\prime}\) denotes the negation of the statement \(s\) $$p \vee r$$

Exercises \(65-78\) deal with propositions in fuzzy logic. Let \(p, q,\) and \(r\) be simple propositions with \(t(p)=1, t(q)=0.3,\) and \(t(r)=\) 0.5 . Compute the truth value of each, where \(s^{\prime}\) denotes the negation of the statement \(s\) . $$ p \vee r $$