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

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. $$(\forall x) \mathrm{P}(x) \rightarrow(\exists x) \mathrm{P}(x)$$

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

Draw a switching network with each representation. $$\left(A \vee B^{\prime}\right) \vee(A \vee B)$$

Draw a switching network with each representation. $$\left(\mathbf{A} \wedge \mathbf{B}^{\prime}\right) \vee\left(\mathbf{A}^{\prime} \wedge \mathbf{B}\right)$$

At the bus terminal, Ellen overheard the following conversation between two baseball fans, L and M: L: I like the Yankees. M: You do not like the Yankees. You like the Dodgers. L: We both like the Dodgers. Does fan L like the Yankees? Who likes the Dodgers?