Set Theory and Proofs

Set and Model Theories

​by

​Sharlynne Vargas
Cindy Fernandez
Alyssa Marie Ibañez

Multiple Choice

It is a fundamental branch of mathematical logic and a foundational theory in mathematics which was developed by .Georg Cantor and Richard Dedekind.

• Model Theory

• Approximation Theory

• Set Theory

• Algebraic K-theory

Multiple Choice

It is a well defined collection of distinct things such as numbers, letters, etc.

• Set

• Element

• Cardinality

• Subset

Multiple Choice

They are used to define a set.

• Parentheses

• Commas

• Braces

• Brackets

Multiple Choice

It refers to each member of a particular set.

• Singleton

• Universal

• Subset

• Element

Multiple Choice

The following are the importance of Set Theory except:

• Sets are used to define the concepts of relations and functions.

• It serves as a foundation for all Mathematics but does not allow you to prove theorems.

• It helps us categorize information.

• It allows us to make sense of a large amount of information by breaking it down into smaller groups.

Multiple Choice

It is a type of set that has no element.
Example: $$B=\left\{prime\ numbers\ between\ 11\ and\ 13\right\}$$

• Infinite Set

• Universal Set

• Null Set

• Singleton Set

Multiple Choice

It is a type of set that is consists of a definite number of elements.
$$A=\left\{primary\ colors\right\}$$

• Finite Set

• Universal Set

• Null Set

• Singleton Set

Multiple Choice

Which among the following figures illustrate

UNION OF SETS?

Multiple Choice

Which among the following figures illustrate

COMPLEMENT OF A SET?

Multiple Choice

If Set P is a set of counting numbers less than 15, then what is the cardinal number of Set P?

• 13

• 15

• 14

• 12

Multiple Choice

It is a branch of mathematical logic that focuses on the study of mathematical structures within the context of formal languages. It explores how these structures can be described, classified, and understood by using the syntax and semantics of first-order logic.

• Model Theory

• Approximation Theory

• Set Theory

• Axiom Theory

Multiple Choice

It is a fundamental theorem for the model theory of classical propositional and first-order logic.

• Completeness Theorem

• Conditional Theorems

• Compactness Theorem

• Sequential Theorem

Multiple Choice

It states that every logically valid formula in first-order logic is provable within the framework of first-order logic. If a statement can be deduced from the axioms of first-order logic using the rules of inference, then it is logically valid.

• Completeness Theorem

• Conditional Theorems

• Compactness Theorem

• Sequential Theorem

Multiple Choice

It is a process that can reduce complex formulas involving quantifiers (like "for all" and "there exists") to simpler ones, making it easier to study models.

• Vaught's Test

• Morley's Categoricity Theorem

• Quantifier Elimination

• Elementary Equivalence

Multiple Choice

This is a criterion used to determine whether a given first-order theory has models of a specific cardinality (size). It helps determine the existence of models of certain sizes for a given theory.

• Vaught's Test

• Morley's Categoricity Theorem

• Quantifier Elimination

• Elementary Equivalence