Name: ______________________________________________________________
Date:__________________ Period:______
Chapter 12: Logic
Topic #2: Compound Statements
Compound Statements:
A _________________________________________ is formed when two or more thoughts are connected in one sentence.
Words such as _____________, _____________, _________________, and ______________________, allow for the formation of
compound statements or sentences.
More than one simple statement is involved in creating compound statements. As a result, more than one
truth value is involved with compound statements.
Let’s Consider the Following Simple Statements:
It is snowing outside.
I shovel my driveway.
From these two simple statements, four basic compound statements can be formed.
1.) It is snowing outside ____________ I shovel my driveway.
2.) It is snowing outside ____________ I shovel my driveway.
3.) _____ it is snowing outside, _________ I shovel my driveway.
4.) It is snowing outside ________________________ I shovel my driveway.
Truth Tables:
Mathematicians often use symbols and tables to represent concepts in logic. This gives us a shorthand
method in evaluating and discussing logical statements.
A truth table is used to summarize the concepts of simple statements. In addition, a truth table will give us
all of the possible outcomes of the truth values of compound statements. p and q are usually used to
represent simple statements within the compound statement.
Conjunction:
In logic, a ___________________is a compound sentence that is formed by combining two simple sentences using
the word "and."
In order for a conjunction to be true, both statements must be true.
If one or more statements are false, then the conjunction is false.
Truth Table For a Conjunction:
Symbol: _____________
p
q
p∧q
Disjunction:
In logic, a ____________________ is a compound statement that is formed by combining ________________ sentences
using the word "__________."
A disjunction is ________________ when ________________ or _____________ simple statements are ______________.
The only time a disjunction is false are when both statements are false.
Symbol: _______
p
q
pVq
Conditional:
In logic, a ___________________ is a ______________________ statement that is created by combining two ______________
statements using the words "______________________." Another name for a conditional is an ______________.
The only time a conditional is ______________ is when the hypothesis (______________ part) is ______________ and the
conclusion (______________ part) is ______________.
Symbol: _______
We read it as: _______________________________
Truth Table for the Conditional:
p
q
p→q
Biconditional:
In logic, a __________________is a compound statement formed by combining two __________________under the word
"__________________." It is formed by the two conditionals: __________________and __________________under a
conjunction "and." It tells us that "p implies q" and "q implies p,” written symbolically as:
______________________.
However, the __________________can be abbreviated by saying "_____________________________."
This is written symbolically as: __________________
The only time a __________________is true is if ____________are the ____________. Either both statements are
____________or both statements are ____________.
If the statements have ____________truth values, then the biconditional is ____________.
Truth Table for Bi-Conditional:
p
q
p↔q
Examples:
Complete the following examples. Show work, when necessary. Circle your answer for multiple choice
questions.
1.) Which compound statement is true?
(1) A triangle has three sides and a square does not have four sides.
(2) A triangle does not have three sides or a square does not have four sides.
(3) If a triangle does not have three sides, then a square has four sides.
(4) A triangle does not have three sides if and only if a square has four sides.
2.) Given: 5 is an odd integer or 4 is an even integer.
Determine the truth value of this disjunction. Justify your answer.
3.) The statement "x is an even integer and x is prime" is true when x is equal to
(1) 1
(2) 2
(3) 5
(4) 6
4.) The statement "x is an even integer or x is a multiple of 5" is false when x is equal to
(1) 5
(2) 10
(3) 15
(4) 21
5.) The statement " x is an odd integer and x is a multiple of 3" is true when x is equal to
(1) 9
(2) 12
(3) 5
(4) 4
6.) Which compound statement is true?
(1) A square has four sides and a pentagon has 6 sides.
(2) A square has four sides or a pentagon has 6 sides.
(3) If a square has four sides, then a pentagon has 6 sides.
(4) A square has four sides if and only if a pentagon has 6 sides.
7.) Given: If two is an even integer, then three is an odd integer.
Determine the truth value of this conditional. Justify your answer.
8.) Given: Three is a prime number if and only if three is not odd.
Determine the truth value of this biconditional. Justify your answer.
Name: ______________________________________________________________
Date:__________________ Period:______
Logic: Compound Statements Homework
Complete the following examples. Circle your answer.
1.) Given the true statements:
“Rebecca plays basketball or tennis.”
“Rebecca does not play tennis.”
Which statement must also be true?
(1) Rebecca plays basketball.
(2) Rebecca does not play basketball.
(3) Rebecca does not play basketball, and she does not play tennis.
(4) Rebecca is a cheerleader.
2.) Which statement is an example of a biconditional statement?
(1) If Joey has money, he buys a car.
(2) Joey buys a car if and only if he has money.
(3) Joey has money or he buys a car.
(4) Joey has money and he buys a car.
3.) The statement “Alexis plays on the basketball team or Alexis joins the ski club” is false. Which statement is
true?
(1) Alexis plays on the basketball team and Alexis joins the ski club.
(2) Alexis plays on the basketball team and Alexis does not join the ski club.
(3) Alexis does not play on the basketball team and Alexis joins the ski club.
(4) Alexis does not play on the basketball team and Alexis does not join the ski club.
4.) Given: “If 10 is a prime number, then 5 is an even number.”
Determine the truth value of this conditional. Justify your answer.
5.) The statement “x is an even number, and x is divisible by 9” is true when x is equal to
(1) 9
(2) 24
(3) 108
(4) 6
Review Questions:
6.) Two angles are complementary. The measure of one angle is 15o more than twice the other. What is the
measure of the smaller angle?
(1) 25o
(2) 35o
(3) 55o
(4) 65o
7.) If the measures, in degrees, of the three angles of a triangle are x, x + 10, and 2x – 6, the triangle must be
(1) isosceles
(2) equilateral
(3) right
(4) scalene
8.) Which transformation produces a figure that is always the mirror image of the original figure?
(1) line reflection
(2) dilation
(3) translation
(4) rotation
9.) The base of an isosceles triangle is 5 and its perimeter is 11. The base of a similar isosceles triangle is 10.
What is the perimeter of the larger triangle?
(1) 15
(2) 21
(3) 22
(4) 110
10.) The imagine of point A after a dilation of 3 is (6,15). What was the original location of point A?
(1) (2,5)
(2) (3,12)
(3) (9,18)
(4) (18,45)
11.) Which letter demonstrates line symmetry but not point symmetry?
(1) T
(2) N
(3) H
(4) S