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, is similar to , 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 and intersect at point E, , and , find the value of x.
8.) Which letter has both line and point symmetry?
(1) B(2) T(3) S(4) H
9.) A line with a slope of passes through the point (3,6). Which point also lines on this line?
(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}