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Propositional and First Order Logic Questions and Answers

Answer: A

Logic underpins verification, planning, database query, description logic reasoning and every application requiring an auditable derivation, while learned methods dominate perception and language. It is neither universal nor obsolete. Judging a tradition by the niches where its properties are indispensable, rather than by its share of attention, gives a fairer and more useful picture of where it should be reached for.

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102.

In the following knowledge representation using first order logic ∀ person Indian (person) ^ know (person, English) ⇒ [Mother tongue (person, lang) ^ hate (person, lang)], the number of predicates and variables are respectively :

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: A

There are 4 predicates and 2 variables.

The predicates are the relation symbols applied to arguments:

  • Indian(person)
  • know(person, English)
  • Mother tongue(person, lang)
  • hate(person, lang)

That makes 4. The variables are person and lang, so 2. English is a constant, not a variable, because it names one particular language.

Counting English as a variable gives 3 (option B), and counting the quantifier or the implication as a predicate gives 5; neither is right.

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Answer: B

A statement is satisfiable if there is some interpretation for which it is true.

In logic, an interpretation assigns truth values (or meanings) to the symbols. A formula is satisfiable if at least one interpretation makes it true, valid if every interpretation makes it true, and unsatisfiable if none does.

Having some interpretation in which it is false makes a formula not valid. No interpretation making it true is unsatisfiability, and no interpretation making it false is validity.

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