How do you define an empty set?

{ } or Ø

Define a “Conjunction” compound statement and its symbol.

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

Define a “Biconditional” statement and its symbol.

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

What is the set of Integers?

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

Ex:

{...-3, -2, -1, 0, 1, 2, 3,...}

Use Inductive Reasoning to predict the next number:

5, 11, 17, 23, 29, __

35.

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

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

Which type of compound statement is:

If 5 > 3, then 2 + 7 = 4

Is it True or False?

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

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

3.

Which type of compound statement is:

4 <= 9

Is it True or False?

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

What compound statement’s symbol is “^”?

A conjunction.

What is the negation of the quantifiers:

All ____ are ____.

The negation of the quantifiers are "some" and "are not".

Define a “Conditional” statement and its symbol.

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

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

2^{4} = 16 rows

What is the complement of the Universe, U?

U′ = Ø (empty set)

What are the quantifiers in the statement:

All dogs are friendly.

What is the statement's negation?

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

What compound statement’s symbol is “v”?

A disjunction.

Define "Inductive Reasoning".

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

What is the negation of the quantifiers:

No(ne) ____.

The negation of the quantifier is "some".

What is a counterexample?

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.

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

2^{3} = 8 rows

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

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

Define "Deductive Reasoning".

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

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

Is A⊆B true or false?

False.

Define a "Subset". How is it denoted?

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

What is a "Cardinal" number?

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

What is the symbol for equivalent compound statements?

≡

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

A conditional statement.

Define a “Disjunction” compound statement and its symbol.

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

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.

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

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

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

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

Quantifiers are only used in negation statements.

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

A "self-contradiction".

Is this statement True or False? If it is False, give a counterexample.

The cube of an odd integer is always an odd number.

The statement is True.

What is the complement of an empty set Ø?

Ø′ = U (the universe).

Which type of compound statement is:

21 is a rational number and 21 is a natural number?

Is it True or False?

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

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.

This is Inductive Reasoning.

What is the set of Whole numbers?

All positive integers including zero.

Ex:

{0, 1, 2, ...}

What is the set of Natural numbers?

All whole numbers greater than zero.

Ex:

{1, 2, 3, ...}

What is an Irrational number?

A number whose terminal digit is unknown.

Ex:

{π, e, √2, √3, ...}

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

A "tautology".

When is homework assigned and due?

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

What is the Grading scale?

Homework and quizzes = 16%

Exams (3 total) = 57%

Final = 27% cumulative

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

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}

Is this statement True or False? If it is False, give a counterexample.

|x + y| = |x| + |y|

The statement is False.

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

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

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}

What is the negation of the quantified statement:

None of the students took math.

The negation is "some students took math".

Define a “negation” compound statement and its symbol.

A negation compound statement is a statement’s opposite. It is denoted by the symbol “~” or the word “not”.

Ex:

P = True

~P = False

What compound statement’s symbol is: ~

A negation.

What is the grade scale of homework and quizzes?

16%.

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

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.

What is the grade scale of the Final Exam?

27%

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

2^{2} = 4 rows.

What is a statement?

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

When is the Final Exam?

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

What compound statement’s symbol is “”?

A biconditional statement.

A = {1, 2} ; B = {1, 2, 4, 6}.

Is A⊆B true or false?

True.

What is a Rational number?

A number whose terminal digit is known.

Ex:

√100, because it = 10.