Set Theory and Mathematical Logic

From the study guide

Course Outline

  1. Propositions and Logical Connectives
  2. Implication and Logical Equivalence
  3. Proof Methods and Induction
  4. Sets and Quantified Statements
  5. Subsets, Equality, and Power Sets
  6. Union and Intersection
  7. Complements and De Morgan Laws
  8. Cartesian Products and Tuples
  9. Families of Sets and Choice

1. Propositions and Logical Connectives

Key Concepts & Definitions

  • Statement: A sentence that has a truth value, true or false.
  • Negation: True when A is false and false when A is true.
  • Conjunction: True exactly when both A and B are true.
  • Disjunction: True when at least one of A and B is true, and false when both are false.
  • Tautology: A statement that is always true.

Essential Points

  • A ∧ ¬A is always false by the principle of non-contradiction, while A ∨ ¬A is always true by the principle of excluded middle.

2. Implication and Logical Equivalence

Key Concepts & Definitions

  • Implication: If whenever A is true, B is true; A is the hypothesis and B is the conclusion.
  • Equivalence: When A ⇒ B and B ⇒ A both hold.
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Practice quiz preview

1. Which feature makes a sentence a proposition in logic?

2. If proposition A is false, what is the truth value of its negation ¬A?

3. A student knows that A is true and B is false; what is the truth value of A ∧ B?

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Flashcard preview

What is a statement in logic?

A sentence with a truth value of true or false.

When is the negation ¬A\neg A true?

When AA is false.

When is the conjunction A∧BA \land B true?

When both AA and BB are true.

When is the disjunction A∨BA \lor B false?

When both AA and BB are false.

What does A⇒BA \Rightarrow B mean?

Whenever AA is true, BB is true.

In A⇒BA \Rightarrow B, what is AA called?

The hypothesis.

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Frequently asked questions

What does the Set Theory and Mathematical Logic study guide cover?

It covers the core concepts of Set Theory and Mathematical Logic, organized by topic with the key definitions, explanations and takeaways, so it's easier to learn and remember.

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How many questions are in the Set Theory and Mathematical Logic quiz?

The practice quiz has 28 multiple-choice questions, each with an explanation. Use it to check what you know and find your gaps.

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How do I study Set Theory and Mathematical Logic with flashcards?

There are 58 flashcards on Set Theory and Mathematical Logic, with a question on the front and the answer on the back. Try to recall each answer before you flip, and let spaced repetition bring back the ones you miss.

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