Name: ______________________________________________________________
Date:__________________ Period:______
Chapter 12: Logic
Topic #1: Logic & Negation Packet
Logic is the study of _____________________ thinking, or _____________________. All reasoning is based on the way that
we put sentences together.
A ___________________________________________ is one in which a fact or complete idea is expressed. Because a
mathematical sentence creates a fact, many of them can be deemed “true” or “false.” Questions or Phrases
are NOT mathematical sentences since they cannot be judged true or false.
Negation
In logic, a _____________________ of a simple statement can usually be formed by placing the word “not” into the
original statement.
The negation will always have the _____________________ truth value as the original statement.
Under a negation, what’s TRUE becomes _____________________ and what’s FALSE becomes _____________________.
The negation of “5 is a prime number” can be written as:
(A) ____________________________________________________________________________
(B) ____________________________________________________________________________
The negation of 2 + 3 = 5 can be written as:
(A) ____________________________________________________________________________
Examples:
Complete the questions below. Show work, when necessary. Circle your answer for multiple choice
questions.
1.) What are the truth values for "Three is an odd number" and its negation?
(1) The statement is true and its negation is true.
(2) The statement is true and its negation is false.
(3) The statement is false and its negation is false.
(4) The statement is false and its negation is true.
2.) A student wrote the statement "7 is a prime number." What is the negation of this sentence and the truth
value of the negation?
(1) 7 is a composite number; true.
(2) 7 is not a prime number; true.
(3) 7 is a composite number; false.
(4) 7 is not a prime number; false.
3.) What is the negation of the statement "I love chocolate chip cookies"?
(1) I love oatmeal cookies.
(2) I think chocolate chip cookies are gross.
(3) It is not the case that I love chocolate chip cookies.
(4) If I eat chocolate chip cookies, then I love them.
4.) Write the negation of "An isosceles triangle has 2 congruent sides," then give the truth value of the
negation.
5.) Given the true statement, "The diagonals bisect in all parallelograms," write the negation of the statement
and give its truth value.
6.) What is the negation of the "Sun is shining"?
(1) The moon is out.
(3) It is raining outside.
(2) The sun is not shining.
(4) If the sun is out, then I am happy.
7.) What is the negation of the statement "A triangle does not have four sides"?
(1) It is not the case that a triangle has four sides.
(2) A triangle has three sides.
(3) A triangle has four sides.
(4) A quadrilateral has four sides.
8.) Write the negation of "22 = 4" then give the truth value of the negation.
9.) Given the statement 100 is a perfect square.
What is the negation and the truth value of the negation?
(1) 100 is not a perfect square; true.
(2) 100 is not a perfect square; false.
(3) 50 is not a perfect square; true.
(4) 50 is a perfect square; false.
Name: ______________________________________________________________
Date:__________________ Period:______
Logic & Negation Homework
Complete the questions below. Circle your answer for multiple choice.
1.) Write the negation of “10 is a prime number” and then state the truth value of the negation.
2.) What is the negation of “Tomorrow is not Sunday”?
(1) Tomorrow is Saturday.
(3) Tomorrow is Sunday.
(2) Yesterday was Sunday.
(4) Yesterday was not Sunday.
3.) Given the statement:
24 is a perfect square.
What is the negation and the truth value of the negation?
(1) 24 is not a perfect square; false.
(3) 24 is not a perfect square; true.
(2) 25 is a perfect square; false.
(4) 25 is not a perfect square; true.
4.) Write the negation of “2 + 3 = 5” and then state the truth value of the negation.
Review Questions:
5.) What is the image of point (-3,7) after a reflection in the x-axis?
(1) (3,7)
(2) (-3,-7)
(3) (3,-7)
(4) (7,-3)
6.) In the accompanying diagram, ∆𝑄𝑅𝑆 is similar to ∆𝐿𝑀𝑁, RQ = 30, QS = 21, SR = 27, and LN = 7. What is the
length of ML?
7.) The support beams on a bridge intersect in the pattern shown in the accompanying diagram. If ̅̅̅̅
𝐴𝐵 and
̅̅̅̅
𝐶𝐷 intersect at point E, 𝑚∠𝐴𝐸𝐷 = 3𝑥 + 30, and 𝑚∠𝐶𝐸𝐵 = 7𝑥 − 10, find the value of x.
8.) Which letter has both line and point symmetry?
(1) B
(2) T
(3) S
(4) H
1
9.) A line with a slope of passes through the point (3,6). Which point also lines on this line?
3
(1) (6,3)
(2) (7,6)
(3) (-3,-3)
(4) (-6,3)
10.) Chris is cutting triangular piece of tile. If the triangle is scalene, which set of numbers could represent
the lengths of the sides?
(1) {2,4,7}
(2) {4,5,6}
(3) {3,5,8}
(4) {5,5,8}