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Discrete Mathematics (Midterms) BSIT 205

Discrete Mathematics (Midterms) BSIT 205
52 questions • 1 y ago
  • Xai Alexandrei Delos Reyes
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    Question list

  • 1

    It is also known as the propositional function or open sentence

    Predicate Logic

  • 2

    Which statement is FALSE about Predicte Logic

    It is commanding statement

  • 3

    Let P(x) denote the statement “x – 3 > 5”. What is the truth value if P(2)

    False

  • 4

    Let a ternary predicate Q(x, y, z) denote the statement “x + y = z”. What is the truth value if Q(25,25,50);

    True

  • 5

    Let Q(x) denote the statement “x is an integer”. What ie the truth value of Q(8/2)

    True

  • 6

    Which Statement is TRUE about the domain of discourse

    It is the set from which the value of the subject x may be chosen for a given P(x)

  • 7

    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

  • 8

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

    ∀

  • 9

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

    ∃

  • 10

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

    Nested Quantifier

  • 11

    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)

  • 12

    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)

  • 13

    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)

  • 14

    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)

  • 15

    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.

  • 16

    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

  • 17

    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

  • 18

    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

  • 19

    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

  • 20

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

    Counterexample

  • 21

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

    ∃x∃y ¬P(x,y)

  • 22

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

    ∀x ¬P(x)

  • 23

    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.

  • 24

    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.

  • 25

    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.

  • 26

    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.

  • 27

    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

  • 28

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

    elements

  • 29

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

    elements

  • 30

    Are sets denoted by upper case/capital letters

    True

  • 31

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

    Universal Set

  • 32

    The number of elements in a set are NOT COUNTABLE

    Infinite Set

  • 33

    The number of elements in a set are COUNTABLE

    Finite Set

  • 34

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

    Set Equality

  • 35

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

    Set Equality

  • 36

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

    Infinite Set

  • 37

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

    Finite Set

  • 38

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

    Subset

  • 39

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

    True

  • 40

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

    Proper Subset

  • 41

    What does this venn diagram represent?

    Set Compliment

  • 42

    What does this venn diagram represent?

    Set Intersection

  • 43

    What does this venn diagram represent?

    Set Union

  • 44

    What does this venn diagram represent?

    Set Difference

  • 45

    What does this venn diagram represent?

    Symmetric Difference

  • 46

    The formula for number of proper subsets of a set with n elements is

    2^n - 1

  • 47

    The formula for number of subsets of a set with n elements is

    2^n

  • 48

    What is the union of sets A = {1, 2, 3} and B = {3, 4, 5}?

    A. {1, 2, 3, 4, 5}

  • 49

    If A = {1, 2, 3, 4, 5} and B = {3, 4}, what is A - B (set difference)?

    {1 ,2, 5}

  • 50

    Given sets A = {1, 2, 3} and B = {2, 3, 4}, find the intersection of A and B.

    B. {2, 3}

  • 51

    What is the complement of set A = {1, 2, 3, 4} in the universal set U = {1, 2, 3, 4, 5}?

    B. {5}

  • 52

    If A = {1, 2, 3} and B = {3, 4, 5}, what is the symmetric difference of sets A and B?

    A {1, 2, 4, 5}

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    Question list

  • 1

    It is also known as the propositional function or open sentence

    Predicate Logic

  • 2

    Which statement is FALSE about Predicte Logic

    It is commanding statement

  • 3

    Let P(x) denote the statement “x – 3 > 5”. What is the truth value if P(2)

    False

  • 4

    Let a ternary predicate Q(x, y, z) denote the statement “x + y = z”. What is the truth value if Q(25,25,50);

    True

  • 5

    Let Q(x) denote the statement “x is an integer”. What ie the truth value of Q(8/2)

    True

  • 6

    Which Statement is TRUE about the domain of discourse

    It is the set from which the value of the subject x may be chosen for a given P(x)

  • 7

    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

  • 8

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

    ∀

  • 9

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

    ∃

  • 10

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

    Nested Quantifier

  • 11

    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)

  • 12

    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)

  • 13

    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)

  • 14

    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)

  • 15

    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.

  • 16

    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

  • 17

    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

  • 18

    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

  • 19

    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

  • 20

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

    Counterexample

  • 21

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

    ∃x∃y ¬P(x,y)

  • 22

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

    ∀x ¬P(x)

  • 23

    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.

  • 24

    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.

  • 25

    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.

  • 26

    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.

  • 27

    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

  • 28

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

    elements

  • 29

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

    elements

  • 30

    Are sets denoted by upper case/capital letters

    True

  • 31

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

    Universal Set

  • 32

    The number of elements in a set are NOT COUNTABLE

    Infinite Set

  • 33

    The number of elements in a set are COUNTABLE

    Finite Set

  • 34

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

    Set Equality

  • 35

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

    Set Equality

  • 36

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

    Infinite Set

  • 37

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

    Finite Set

  • 38

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

    Subset

  • 39

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

    True

  • 40

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

    Proper Subset

  • 41

    What does this venn diagram represent?

    Set Compliment

  • 42

    What does this venn diagram represent?

    Set Intersection

  • 43

    What does this venn diagram represent?

    Set Union

  • 44

    What does this venn diagram represent?

    Set Difference

  • 45

    What does this venn diagram represent?

    Symmetric Difference

  • 46

    The formula for number of proper subsets of a set with n elements is

    2^n - 1

  • 47

    The formula for number of subsets of a set with n elements is

    2^n

  • 48

    What is the union of sets A = {1, 2, 3} and B = {3, 4, 5}?

    A. {1, 2, 3, 4, 5}

  • 49

    If A = {1, 2, 3, 4, 5} and B = {3, 4}, what is A - B (set difference)?

    {1 ,2, 5}

  • 50

    Given sets A = {1, 2, 3} and B = {2, 3, 4}, find the intersection of A and B.

    B. {2, 3}

  • 51

    What is the complement of set A = {1, 2, 3, 4} in the universal set U = {1, 2, 3, 4, 5}?

    B. {5}

  • 52

    If A = {1, 2, 3} and B = {3, 4, 5}, what is the symmetric difference of sets A and B?

    A {1, 2, 4, 5}