It expresses the extent to which a predicate P is TRUE (or FALSE) for ALL possible values in the universe of discourse or for SOME value(s) in the universe of discourse

Quantifiers

It is represented by ", which means “FOR ALL”

∀

It is represented by $, which means “THERE EXISTS”

∃

It is a quantifier that appears within the scope of another quantifier

Nested Quantifier

For every real number x and for every real number y, x + y = 5. Which is the correct expression of this sentence as a Nested quantifier?

∀x∀yP(x,y)

There exists a real number x and a real number y such that x + y = 5. Which is the correct expression of this sentence as a Nested quantifier?

∃x∃yP(x,y)

For all real numbers x, there exists a real number y such that x + y = 5. Which is the correct expression of this sentence as a Nested quantifier?

∀x∃yP(x,y)

There exists real numbers x, for all real numbers y such that x + y = 5. Which is the correct expression of this sentence as a Nested quantifier?

∃x∀yP(x,y)

Let P (x,y) be the statement “Student x has taken class y”, where the domain for x consists of ALL STUDENTS and y consists of ALL COMPUTER ENGINEERING COURSES at your school ∀x∀yP(x,y) What is the correct English expression of this Nested Quantifier?

All Students has taken every computer engineering course.

Let the DOMAIN of x and y be real numbers P(x,y) denotes "x + y = 0" What is the truth value of ∀x∀yP(x,y)

False

Let the DOMAIN of x and y be real numbers P(x,y) denotes "x + y = 0" What is the truth value of the ∃x∀yP(x,y)

False

Let the DOMAIN of x and y be real numbers P(x,y) denotes "x + y = 0" What is the truth value of the ∀x∃yP(x,y)

True

Let the DOMAIN of x and y be real numbers P(x,y) denotes "x + y = 0" What is the truth value of the ∃x∃yP(x,y)

True

It is an element/object for which P(x) is FALSE

Counterexample

What is the Negation of this expression ∀x∀yP(x,y)

∃x∃y ¬P(x,y)

What is the Negation of this expression ∃xP(x)

∀x ¬P(x)

Let P(x,y) be the statement "x hates y" The DOMAIN of both x and y consists of all the people in the world ∀x∀yP(x,y) What is the English translation of these Quantifiers?

Everyone hates everyone.

Let P(x,y) be the statement "x hates y" The DOMAIN of both x and y consists of all the people in the world ∀x∃yP(x,y) What is the English translation of these Quantifiers?

For everyone, everyone hates someone.

Let P(x,y) be the statement "x hates y" The DOMAIN of both x and y consists of all the people in the world ∃x∀yP(x,y) What is the English translation of these Quantifiers?

There is someone who hates everyone.

Let P(x,y) be the statement "x hates y" The DOMAIN of both x and y consists of all the people in the world ∃x∃yP(x,y) What is the English translation of these Quantifiers?

Someone hates them.

It is a well-defined and an unordered collection/aggregate of objects of any kind; the objects are referred as elements, or members of the set

Set

The objects in a set are referred as ______, or members of the set

elements

The objects in a set are referred as ______, or members of the set

elements

Are sets denoted by upper case/capital letters

True

It is the set that contains all elements relevant to a particular discussion or problem

Universal Set

The number of elements in a set are NOT COUNTABLE

Infinite Set

The number of elements in a set are COUNTABLE

Finite Set

It states that the two (2) given sets are identical, if and only if they contain EXACTLY THE SAME elements

Set Equality

A = {9, 2, 7, -3}, B = {7, 9, -3, 2} Is an example of?

Set Equality

{...0,1,2,3,4} Is an example of?

Infinite Set

{cats,dogs,...,pigs,cows} Is an example of?

Finite Set

It is a set contained in a larger set or in an equal set

Subset

Determine whether set A is a subset of set B A = {rain, snow, sleet} B = { rain, snow, sleet, hail }

True

It is a subset that is not equal to the set it belongs to

Proper Subset