General Mathematics I Lecture Notes

These flashcards cover foundational concepts in set theory and number systems as outlined in the lecture notes for General Mathematics I.

What does elementary set theory define?

It defines a set and provides examples along with standard notation.

Define a set according to the lecture notes.

A set is a well-defined collection of objects, where it's possible to determine membership.

What is the significance of Venn diagrams in set theory?

Venn diagrams are used to visualize operations on sets.

What is the formula for the union of two sets A and B?

The union A ∪ B is the collection of all elements that are in A, B, or both.

What is the difference between a finite set and an infinite set?

A finite set has a limited number of elements, whereas an infinite set has an unlimited number of elements.

What is the concept of the empty set?

The empty set is a set that contains no elements, denoted by {} or ∅.

What are the properties of relations introduced in the lecture?

Reflexive, symmetric, and transitive properties of relations.

What does the cardinality of a set represent?

The number of elements in a set.

How is a function defined in the context of relations?

A function is a special type of relation that assigns each element of a set exactly one element of another set.

What is De Morgan's law in set theory?

It describes how complements of unions and intersections relate to each other.

What is a Gaussian elimination?

A method used to solve systems of linear equations or to find rank.

What are the basic arithmetic operations defined on sets?

Union, intersection, difference, and complement.