Quiz 1

Question 1

How do you define an empty set?

Answer 1

{ } or Ø

Question 2

Define a “Conjunction” compound statement and its symbol.

Answer 2

A conjunction compound statement means if any statement is False, the whole thing is false. It is denoted by a big “^” symbol or the word “and”.

Ex:

P = True

Q = False

P ^ Q = False

Question 3

Define a “Biconditional” statement and its symbol.

Answer 3

A biconditional statement is only True if both statements are the equal. It is denoted by the symbol “<–>” or the format “if and only if”.

Ex:

P = False

Q = False

P <–> Q = True

Question 4

What is the set of Integers?

Answer 4

The set of Integers is all whole numbers that are positive, negative, or zero.

Ex:

{…-3, -2, -1, 0, 1, 2, 3,…}

Question 5

Use Inductive Reasoning to predict the next number:

5, 11, 17, 23, 29, __

Answer 5

35.

Question 6

What is the set of negative integers between -5 and +6?

Answer 6

{-4, -3, -2, -1}

Question 7

Which type of compound statement is:

If 5 > 3, then 2 + 7 = 4

Is it True or False?

Answer 7

It is a conditional statement (if…, then…), and it is False.

Question 8

How many exams (not including final) will be given?

Answer 8

3.

Question 9

Which type of compound statement is:

4 <= 9

Is it True or False?

Answer 9

It is a disjunction (or), and it is True.

Question 10

What compound statement’s symbol is “^”?

Answer 10

A conjunction.

Question 11

What is the negation of the quantifiers:

All ____ are ____.

Answer 11

The negation of the quantifiers are “some” and “are not”.

Question 12

Define a “Conditional” statement and its symbol.

Answer 12

A conditional statement follows the conclusion’s result*. It is denoted by the “—>” symbol or the format “If…, (then)…” (Hypothesis —> Conclusion).

* Besides (F —> F), which is True.

Ex:

P = True

Q = False

P —> Q = Conclusion (Q) = False

Question 13

How many rows are in a Truth Table with 4 variables?

Answer 13

2⁴ = 16 rows

Question 14

What is the complement of the Universe, U?

Answer 14

U′ = Ø (empty set)

Question 15

What are the quantifiers in the statement:

All dogs are friendly.

What is the statement’s negation?

Answer 15

The quantifiers are the words “all” and “are”. The negation of the statement is “Some dogs are not friendly”.

Question 16

What compound statement’s symbol is “v”?

Answer 16

A disjunction.

Question 17

Define “Inductive Reasoning”.

Answer 17

It is the process of reaching a general conclusion by examining specific examples. (pattern, specific -> general)

Question 18

What is the negation of the quantifiers:

No(ne) ____.

Answer 18

The negation of the quantifier is “some”.

Question 19

What is a counterexample?

Answer 19

If you can find one case for which statement is not true, then it is called a counterexample.

Ex:

x + x > x. FALSE

c.e.: x=0, 0+0 is not greater than 0.

Question 20

How many rows are in a Truth Table with 3 variables?

Answer 20

2³ = 8 rows

Question 21

What is the set of counting numbers larger than 11 and less than or equal to 19?

Answer 21

{12, 13, 14, 15, 16, 17, 18, 19}

Question 22

Define “Deductive Reasoning”.

Answer 22

It is the process of reaching a conclusion by applying general assumptions, procedures, or principles. (general –> specific)

Question 23

A = {1, 2, 3, 4, 5} ; B = {2, 3, 4, 5}

Is A⊆B true or false?

Answer 23

False.

Question 24

Define a “Subset”. How is it denoted?

Answer 24

A is a subset of B, if and only if every element of A is also an element of B. It is denoted by the symbol “⊆”.

Ex:

A = {2, 3, 4} ; B = {2, 3, 4, 5}

A⊆B = True

Question 25

What is a "Cardinal" number?

Answer 25

The cardinal number is the total number of elements in a set.

Question 26

What is the symbol for equivalent compound statements?

Answer 26

≡

Question 27

What compound statement’s symbol is “—\>”?

Answer 27

A conditional statement.

Question 28

Define a “Disjunction” compound statement and its symbol.

Answer 28

A disjunction compound statement means that if any statement is True, the whole thing is True. It is denoted by the symbol “v” or the word “or”. Ex: P = True Q = False P v Q = True

Question 29

Is this Inductive or Deductive reasoning? All Janet novels are worth reading. The novel "To The Nines" is a Janet novel. Thus "To The Nines" is worth reading.

Answer 29

This is Deductive Reasoning. "All" is general --\> "To The Nines" is specific.

Question 30

What is the "Intersection" of sets? What is its symbol?

Answer 30

The intersection of sets is the set of their common elements. It is denoted by "∩". Ex: A = {2, 4, 6} B = {1, 3, 5, 7} C = {6, 8} A∩B = { } or Ø

Question 31

In what type of compound statements are "Quantifiers" used?

Answer 31

Quantifiers are only used in negation statements.

Question 32

What do you call it if all results of a Truth Table are False?

Answer 32

A "self-contradiction".

Question 33

Is this statement True or False? If it is False, give a counterexample. The cube of an odd integer is always an odd number.

Answer 33

The statement is True.

Question 34

What is the complement of an empty set Ø?

Answer 34

Ø′ = U (the universe).

Question 35

Which type of compound statement is: 21 is a rational number and 21 is a natural number? Is it True or False?

Answer 35

It is a conjunction (and), and it is True.

Question 36

Is this Inductive or Deductive reasoning? During the past 10 years, a tree has produced plums every other year. Last year the tree did not produce plums, so this year the tree will produce plums.

Answer 36

This is Inductive Reasoning.

Question 37

What is the set of Whole numbers?

Answer 37

All positive integers including zero. Ex: {0, 1, 2, ...}

Question 38

What is the set of Natural numbers?

Answer 38

All whole numbers greater than zero. Ex: {1, 2, 3, ...}

Question 39

What is an Irrational number?

Answer 39

A number whose terminal digit is unknown. Ex: {π, e, √2, √3, ...}

Question 40

What do you call it if all results of a Truth Table are True?

Answer 40

A "tautology".

Question 41

When is homework assigned and due?

Answer 41

Homework is assigned at the end of each class and **due before each test**.

Question 42

What is the Grading scale?

Answer 42

Homework and quizzes = 16% Exams (3 total) = 57% Final = 27% cumulative

Question 43

What is the "Union" of sets? What is its symbol?

Answer 43

The Union of sets is the set of all elements in the sets. It is denoted by "∪". Ex: A = {2, 4, 6} B = {1, 3, 5, 7} C = {6, 8} A∪B = {1, 2, 3, 4, 5, 6, 7}

Question 44

Is this statement True or False? If it is False, give a counterexample. |x + y| = |x| + |y|

Answer 44

The statement is False. c.e. : x = -3, y = -5, |-3+5| does not equal |-3| + |5|. 2 is not = to 8.

Question 45

What is the "complement" of a set? How is it denoted?

Answer 45

It is the opposite. It is denoted by the "prime" symbol, " ′ ". Ex: U = {1, 2, 3, 4, 5} ; A = {2, 5} A′ = {1, 3, 4}

Question 46

What is the negation of the quantified statement: None of the students took math.

Answer 46

The negation is "some students took math".

Question 47

Define a “negation” compound statement and its symbol.

Answer 47

A negation compound statement is a statement’s opposite. It is denoted by the symbol “~” or the word “not”. Ex: P = True ~P = False

Question 48

What compound statement’s symbol is: ~

Answer 48

A negation.

Question 49

What is the grade scale of homework and quizzes?

Answer 49

16%.

Question 50

What is a "Proper Subset"? How is it denoted?

Answer 50

Same as a subset besides excluding equal sets. A cannot equal B. It is denoted by the symbol "⊂". Ex: A = {1, 2} ; B = {1, 2} A⊂B = False.

Question 51

What is the grade scale of the Final Exam?

Answer 51

27%

Question 52

How many rows are in a Truth Table with 2 variables?

Answer 52

2² = 4 rows.

Question 53

What is a statement?

Answer 53

A statement is a sentence that is either true or false but not both simultaneously. A statement cannot be a question, command, or personal opinion. Ex: The word “cat” has three letters. x + 1 = 6

Question 54

When is the Final Exam?

Answer 54

The Final Exam will be on **Thursday, July 26th**.

Question 55

What compound statement’s symbol is “\<--\>”?

Answer 55

A biconditional statement.

Question 56

A = {1, 2} ; B = {1, 2, 4, 6}. Is A⊆B true or false?

Answer 56

True.

Question 57

What is a Rational number?

Answer 57

A number whose terminal digit is known. Ex: √100, because it = 10.