Exploring Sets and Logic Concepts

What is a set? Provide an example.

• A set is a collection of distinct objects. Example: {a, e, i, o, u}.

• A set is a random assortment of items. Example: {apple, banana, orange, apple}

• A set is a single object. Example: {1}

• A set is a collection of similar objects. Example: {1, 1, 1}

Define a subset and give an example.

• A = {1, 2, 3} is a subset of B = {1, 2}

• E = {1, 2, 3} is a subset of F = {1, 2, 3, 4}

• An example of a subset is B = {1, 2} which is a subset of A = {1, 2, 3}.

• C = {4, 5} is a subset of D = {1, 2, 3}

What is a powerset? How is it calculated?

• The powerset includes only the empty set, calculated as 1

• The powerset of a set is the set of all its subsets, calculated as 2^n.

• The powerset is the set of all elements in a set, calculated as n!

• The powerset is the set of unique elements, calculated as n^2

Explain the union operation on sets with an example.A={1,2,3}, B={4,5}

• {4, 5}

• {1, 2, 3, 4, 5, 6}

• {1, 2, 3, 4, 5}

• {1, 2, 3}

What is the intersection of two sets? Provide an example.a={1,2,3}, B={2,3,4}

• {2, 5}

• {2, 3}

• {1, 4}

• {3, 6}

Define propositional logic and its components.

• Propositional logic only deals with numerical values.

• Propositional logic is a formal system in logic that represents statements using propositions and logical connectives.

• Propositional logic is a type of programming language.

• Propositional logic is unrelated to logical connectives.

What are the rules of inference in propositional logic?

• Affirming the Consequent

• Transitive Property

• Modus Ponens, Modus Tollens, Disjunctive Syllogism, Hypothetical Syllogism, Conjunction, Simplification

• Denying the Antecedent

Explain the difference between universal and existential quantifiers.

• Universal quantifiers assert properties for all elements; existential quantifiers assert properties for at least one element.

• Universal quantifiers can be negated; existential quantifiers cannot be negated.

• Universal quantifiers are used only in logic; existential quantifiers are used in mathematics.

• Universal quantifiers apply to some elements; existential quantifiers apply to none.

What is a predicate in logic? Give an example.

• Example of a predicate: 'x + y = 10'.

• A predicate in logic is a statement that can be true or false depending on the values of its variables. Example: 'P(x) = x is even'.

• A predicate is always true regardless of its variables.

• A predicate is a type of logical operator.

What does it mean for a statement to be valid in predicate logic?

• A statement is valid if it contains no variables.

• A statement is valid if it is false in at least one interpretation.

• A statement is valid if it is true in some interpretations only.

• A statement is valid in predicate logic if it is true in every interpretation.