Discrete Mathematics - Vol 1 | 10. Proof Strategies-I by Abraham | Learn Smarter
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10. Proof Strategies-I

The chapter introduces various proof strategies, focusing on direct proofs and several methods of indirect proof including proof by contrapositive, vacuous proof, and proof by contradiction. These proof methods are essential for validating universally quantified implications in mathematics. Examples and illustrations clarify how each strategy can be applied effectively in different contexts.

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Sections

  • 10.1

    Discrete Mathematics

    This section introduces various proof strategies in discrete mathematics, including direct proofs and forms of indirect proof.

    Learning Practice

  • 10.1.1

    Proof Strategies-I

    This section introduces various proof strategies in discrete mathematics, including direct proofs and forms of indirect proofs such as proof by contrapositive, vacuous proof, and proof by contradiction.

    Learning Practice

  • 10.1.2

    Direct Proof Method

    This section explores the direct proof method in mathematical logic, explaining how to prove universally quantified implications and the conditions in which indirect proof methods may be necessary.

    Learning Practice

  • 10.1.3

    Indirect Proof Methods

    This section introduces indirect proof methods, including proof by contrapositive, vacuous proof, and proof by contradiction, as alternatives to direct proofs.

    Learning Practice

  • 10.1.3.1

    Proof By Contraposition

    This section introduces proof by contraposition, an indirect proof method used to validate implications through negation.

    Learning Practice

  • 10.1.3.2

    Vacuous Proof

    This section delves into vacuous proof, a crucial indirect proof technique that shows an implication is true when its premise is false, regardless of the validity of its conclusion.

    Learning Practice

  • 10.1.3.3

    Proof By Contradiction

    Proof by contradiction is a method that shows the truth of an implication by assuming the contrary leads to a false conclusion.

    Learning Practice

  • 10.1.3.3.1

    Using Proof By Contradiction For Single Proposition

    This section explains the proof by contradiction method for establishing the truth of a single proposition.

    Learning Practice

  • 10.2

    Conclusion

    This section summarizes the proof strategies used in discrete mathematics, including direct proofs and various forms of indirect proofs.

    Learning Practice

  • 10.2.1

    Summary Of Proof Methods

    This section introduces various proof strategies, including direct proofs and several indirect proof methods.

    Learning Practice

References

ch10.pdf

Class Notes

Memorization

What we have learnt

  • Different proof strategies ...
  • Direct proof starts by assu...
  • Indirect proof methods are ...

Final Test

Revision Tests