Practice Existential Quantification Example - 9.5.1 | 9. Rules of Inferences in Predicate Logic - part A | Discrete Mathematics - Vol 1
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9.5.1 - Existential Quantification Example

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What does S(x) represent in the context of the given examples?

💡 Hint: Think about what the statement is inferring about students.

Question 2

Easy

What is the difference between 'for all x, S(x) ∧ C(x)' and 'for all x, S(x) → C(x)'?

💡 Hint: Focus on the implications of each statement.

Practice 4 more questions and get performance evaluation

Interactive Quizzes

Engage in quick quizzes to reinforce what you've learned and check your comprehension.

Question 1

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))

💡 Hint: Focus on the implications.

Question 2

Is the statement 'There exists some x such that S(x) ∧ C(x)' true if no students are in CS201?

  • True
  • False

💡 Hint: Revisit the meaning of 'some student'.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

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.

💡 Hint: Assess the total students in CS201 and how they relate to the predicates defined.

Question 2

Formulate a logical expression for 'No students in CS201 have failed calculus' and discuss how it can be represented differently.

💡 Hint: Explore negation in existential quantification and its conversion to universal quantification.

Challenge and get performance evaluation