Discrete Mathematics - Vol 1 | 13. Lecture - 13 by Abraham | Learn Smarter
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13. Lecture - 13

The chapter focuses on logical arguments, predicates, and quantifiers in discrete mathematics, demonstrating how to analyze arguments for validity using counterexamples. It covers the significance of establishing precise definitions through predicates, alongside practical exercises for expressing mathematical statements about collections. The exploration extends to the properties of real numbers and proofs regarding the existence of prime numbers.

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Sections

  • 13.1

    Discrete Mathematics

    This section introduces key concepts in discrete mathematics, including predicates, quantifiers, and validity of arguments.

    Learning Practice

  • 13.1.1

    Lecture - 13

    In this section, Prof. Ashish Choudhury discusses logical arguments in discrete mathematics, focusing on validity, predicates, and examples demonstrating these concepts.

    Learning Practice

  • 13.1.2

    Tutorial 2: Part 1

    This section discusses the validity of logical arguments in discrete mathematics, illustrating concepts with examples involving predicates and quantifiers.

    Learning Practice

  • 13.2

    Question 1

    This section discusses the validity of arguments based on premises within predicate logic.

    Learning Practice

  • 13.3

    Question 2

    In this section, students learn how to express logical statements using predicate functions, focusing on a specific example regarding stamp collectors and contributions from African countries.

    Learning Practice

  • 13.4

    Question 3

    This section delves into the nature of predicates and their implications, alongside example problems that explore the validity of logical arguments.

    Learning Practice

  • 13.4.1

    Part A

    This section explores predicate logic by examining the validity of arguments and predicates in mathematical reasoning.

    Learning Practice

  • 13.4.2

    Part B

    This section discusses the validation of logical arguments using predicate functions and introduces examples of expressing specific conditions and analyzing the truth of propositions.

    Learning Practice

  • 13.5

    Question 4

    In this section, we explore implications involving quantified expressions, specifically their validity and how to prove or disprove them.

    Learning Practice

  • 13.5.1

    Part A

    This section covers the validity of logical arguments and demonstrates how to express logical statements using predicates.

    Learning Practice

  • 13.5.2

    Part B

    This section analyzes logical arguments using predicate functions and identifies valid and invalid reasoning through examples and counterexamples.

    Learning Practice

  • 13.6

    Question 5

    The section explores the proof of the infinitude of prime numbers through contradiction, using a number defined as the product of known primes plus one.

    Learning Practice

  • 13.7

    Question 6

    This section demonstrates that among any set of real numbers, at least one number is guaranteed to be greater than or equal to the average.

    Learning Practice

  • 13.8

    Question 7

    In this section, we prove that in any arbitrary arrangement of numbers from 1 to 10, there exists a set of three consecutive integers whose sum is greater than or equal to 17.

    Learning Practice

References

ch13.pdf

Class Notes

Memorization

What we have learnt

  • Arguments can be evaluated ...
  • Existential and universal q...
  • Counterexamples are crucial...

Final Test

Revision Tests