Book contents
- Frontmatter
- Contents
- Preface
- I Study skills for mathematicians
- II How to think logically
- 6 Making a statement
- 7 Implications
- 8 Finer points concerning implications
- 9 Converse and equivalence
- 10 Quantifiers – For all and There exists
- 11 Complexity and negation of quantifiers
- 12 Examples and counterexamples
- 13 Summary of logic
- III Definitions, theorems and proofs
- IV Techniques of proof
- V Mathematics that all good mathematicians need
- VI Closing remarks
- Appendices
- Index
This chapter is part of a book that is no longer available to purchase from Cambridge Core
13 - Summary of logic
from II - How to think logically
Book contents
- Frontmatter
- Contents
- Preface
- I Study skills for mathematicians
- II How to think logically
- 6 Making a statement
- 7 Implications
- 8 Finer points concerning implications
- 9 Converse and equivalence
- 10 Quantifiers – For all and There exists
- 11 Complexity and negation of quantifiers
- 12 Examples and counterexamples
- 13 Summary of logic
- III Definitions, theorems and proofs
- IV Techniques of proof
- V Mathematics that all good mathematicians need
- VI Closing remarks
- Appendices
- Index
Summary
A summary of ways of writing statement A implies statement B
A implies B.
A is true implies B is true.
A ⇒ B.
If A, then B.
If A, B.
B if A.
A only if B.
A is sufficient for B.
B is necessary for A.
Either A is false or B is true.
Ways of writing statement A is equivalent to statement B
A is equivalent to B.
A ⇔ B.
A if and only if B.
A is necessary and sufficient for B.
- Type
- Chapter
- Information
- How to Think Like a MathematicianA Companion to Undergraduate Mathematics, pp. 96Publisher: Cambridge University PressPrint publication year: 2009