Practice Existential Quantification Example (9.5.1) - Rules of Inferences in Predicate Logic - part A

Practice: Existential Quantification Example

Lesson 9.5.1Rules of Inferences in Predicate Logic - part A

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9 questions

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4 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What does S(x) represent in the context of the given examples?
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Think about what the statement is inferring about students.
Question 2.
What is the difference between 'for all x, S(x) ∧ C(x)' and 'for all x, S(x) → C(x)'?
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Focus on the implications of each statement.
3Question 3.
What is the correct representation of 'Every student in CS201 has studied calculus'?
- ∀x (S(x) ∧ C(x))
- ∀x (S(x) → C(x))
- ∃x (S(x) ∧ C(x))
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Focus on the implications.
4Question 4.
Is the statement 'There exists some x such that S(x) ∧ C(x)' true if no students are in CS201?
- True
- False
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Revisit the meaning of 'some student'.
Question 5.
Given a university with 100 students, construct a scenario demonstrating the difference between 'some students are taking CS201' and 'all students are taking CS201' using predicates.
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Assess the total students in CS201 and how they relate to the predicates defined.
Question 6.
Formulate a logical expression for 'No students in CS201 have failed calculus' and discuss how it can be represented differently.
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Explore negation in existential quantification and its conversion to universal quantification.

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