Consider the following statements Anyone passing his math exams and winning the lottery is happy. Anyone who studies or is lucky can pass all his exams. Ravi did not study but he is lucky. Anyone who is lucky wins the lottery. Translate these sentences into predicate logic form. Convert them to Conjunctive Normal Form(CNF) if required. Prove by resolution that Ravi is happy

Translate the following statements into logical expressions using predicates, quantifiers, and logical connectives. Predicates: C(x): x is a CSE student L(x): x loves music The universe of discourse for the variable x is all students. a. Every student loves music b. No student loves music c. Some students love music d. Every CSE student loves music e. Some CSE students love music

Which can be converted to inferred equivalent CNF sentence? A. Every sentence of propositional logic B. Every sentence of inference C. Every sentence of first-order logic D. All of the mentioned

Express each of these statements using predicates with two variables andnested quantifiers. Then form the negation of the statement so that no negation is to the left ofa quantifier. Next, express the negation in simple English. (Do not simply use the phrase “It isnot the case that.”)a) Every Ashesi student has taken some math course.b) No one knows everybody

Let 𝑝 and 𝑞 be the proposition variables denoting𝑝: It is below freezing.𝑞: It is snowing.Write the following propositions using variables, 𝑝 and 𝑞, and logical connectives.a. It is below freezing and snowingb. It is below freezing but not snowingc. It is not below freezing and it is not snowing.d. It is either snowing or below freezing (or both).e. If it is below freezing, it is also snowing.f. It is either below freezing or it is snowing, but it is not snowing if itis below freezing.g. That it is below freezing is necessary and sufficient for it to besnowing

1. Select the pair of sentences that relate logically with the given statement: Either Swetha is sick or she is careless.a) Swetha is not sickb) Swetha is not carelessc) Swetha is Sickd) Swetha is careless daabbaad