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Magazine Problem 67
Determine the truth value of each, where \(P(s)\) denotes an arbitrary predicate. $$(\exists ! x) P(x) \rightarrow(\exists ! y) P(y)$$
Problem 68
Define the quantifier \(\exists !\) in terms of the quantifiers \(\exists\) and \(\forall\).
Problem 68
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 \(s\) $$q \vee q^{\prime}$$
Problem 68
Indicate the order in which each logical expression is evaluated by properly grouping the operands using parentheses. $$p \vee q \leftrightarrow \sim p \wedge \sim q$$
Problem 68
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 \(s\) . $$ q \vee q $$
Problem 69
Indicate the order in which each logical expression is evaluated by properly grouping the operands using parentheses. $$p \rightarrow q \leftrightarrow \sim p \vee q$$
Problem 70
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 \(s\) . $$ p^{\prime} \vee q $$
Problem 70
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 \(s\) $$p^{\prime} \vee q$$
Problem 71
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 \(s\) $$(p \wedge q)^{\prime}$$
Problem 71
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 \(s\) . $$ (p \wedge q)^{\prime} $$
