Practice Disproving Universally Quantified Statements - 11.1 | 11. Proof Strategies-II | Discrete Mathematics - Vol 1
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge

11.1 - Disproving Universally Quantified Statements

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define a counterexample in the context of universally quantified statements.

💡 Hint: Think about why one example is enough to disprove an assertion.

Question 2

Easy

What does 'proof by cases' entail?

💡 Hint: Consider whether all potential scenarios have been addressed.

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 a counterexample in the context of disproving a universally quantified statement?

  • A statement that supports the universal claim.
  • An example that showcases a case where the universal claim does not hold.
  • A proof of the universal claim.

💡 Hint: Think about scenarios where a universal claim fails.

Question 2

True or False: Proof by cases means you only need to prove one scenario.

  • True
  • False

💡 Hint: Consider how many cases you must consider.

Solve 3 more questions and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Explore whether the statement 'All prime numbers are odd' is valid. Provide a counterexample, and analyze the implications of proving such a statement false.

💡 Hint: Look for the simplest prime numbers.

Question 2

Demonstrate how proof by cases could simplify proving the inequality a² > b² for positive integers. Break down the analysis into relevant cases.

💡 Hint: Think about expressions that exhibit these properties.

Challenge and get performance evaluation