91Ó°ÊÓ

Suppose that the domain of discourse of the propositional function \(P\) is \(\\{1,2,3,4\\} .\) Rewrite each propositional function using only negation, disjunction, and conjunction. $$ \exists x \neg P(x) $$

Write the truth table of each proposition. $$ \left(b_{\llcorner} \wedge d_{\llcorner}\right) \vee\left(b_{\llcorner} \wedge d\right) \vee\left(b \wedge d_{\llcorner}\right) \vee(b \wedge d) $$

What is the cardinality of \(\\{\varnothing\\} ?\)

Tell which rule of inference is used. Fishing is a popular sport or lacrosse is wildly popular in California. Lacrosse is not wildly popular in California. Therefore, fishing is a popular sport.

Give an argument using rules of inference to show that the conclusion follows from the hypotheses. Hypotheses: If there is gas in the car, then I will go to the store. If I go to the store, then I will get a soda. There is gas in the car. Conclusion: I will get a soda.

Refer to the propositions \(p, q,\) and \(r ; p\) is true, \(q\) is false, and r's status is unknown at this time. Tell whether each proposition is true, is false, or has unknown status at this time. $$ (p \vee r) \leftrightarrow r $$

Write the truth table of each proposition. $$ \neg(p \wedge q) \vee(\neg q \vee r) $$

Suppose that the domain of discourse of the propositional function \(P\) is \(\\{1,2,3,4\\} .\) Rewrite each propositional function using only negation, disjunction, and conjunction. $$ \neg(\exists x P(x)) $$

What is the cardinality of \(\\{a, b, a, c\\} ?\)

Suppose that the domain of discourse of the propositional function \(P\) is \(\\{1,2,3,4\\} .\) Rewrite each propositional function using only negation, disjunction, and conjunction. $$ \forall x((x \neq 1) \rightarrow P(x)) $$