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Logic Worksheet
Classwork/Homework #1 (due Fri)
NEGATIONS
In 1 – 4, write the negation of each sentence.
1) The school has a cafeteria.
2) Georgia is not a city.
3) Today is not Saturday.
4) The measure of a right angle is 90 degrees.
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In 5 – 8, for each given sentence: a) Write the sentence in symbolic form, using the symbols
shown below. b) Then tell if the sentence is true, false, or open.
Let p represent “A cat is an animal.”
Let q represent “A poodle is a cat.”
Let r represent “His cat is gray.”
5) A cat is an animal.
6) A poodle is not a cat.
7) His cat is not gray.
8) It is not the case that a cat is not an animal.
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In 9 - 14, the symbols represent sentences.
p: “Summer follows spring.”
q: “Baseball is a sport.”
r: “Baseball is a summer sport.”
s: “ He likes baseball.”
a) Write a complete sentence in words, b) Tell if the sentence is true, false, or open.
9) ~ p
10) ~ q
11) ~ r
12) ~ s
13) ~ (~ q)
14) ~ (~ p)
9) ____________________________________________________________________
10) ____________________________________________________________________
11) ____________________________________________________________________
12) ____________________________________________________________________
13) ____________________________________________________________________
14) ____________________________________________________________________
In 15 – 18, Use the domain {square, triangle, rectangle, parallelogram, rhombus, trapezoid} to
find the truth set for each open sentence:
15) It has three and only three sides
16) It has interior angles with measures whose sum is 360-degrees
17) It contains only right angles
18) It has exactly six sides
Classwork/Homework #2 (due Mon) CONJUNCTIONS &
DISJUNCTIONS
In 1 – 5, determine the truth-value
1) Five is an even number and five is a prime number
2) A square is a rectangle or a triangle has three sides
3) Let p represent "2x + 2 = 12" and q represent "2x + 3x =30." What is the truth-value of p
and q when x = 5?
4) Given the true statements: "t is a multiple of 3" and "t is even." What could be a value of t?
(1) 8
(2) 15
(3) 9
(4) 24
5) The statement "x is divisible by 5 or x is divisible by 4" is false when x equals
(1) 10
(2) 20
(3) 16
(4) 27
In 6 – 7 , substitute values of the domain to find the truth set for the open sentence
6) Use the domain {1, 2, 3, 4} and determine the truth value: (x < 3)
(x is a prime)
7) Use the domain {1, 2, 3, 4, 5, 6, 7, 8} and determine the truth value: (x > 3)
(x is odd)
In 8 – 12, write as a compound sentence. Determine the truth-value.
Let p: “Every line segment has a midpoint”
q: “A line has a midpoint”
Let r: “A ray has one endpoint”
8. q  r
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9. p  ~q
10. ~r  ~q
11. ~p  q
12. ~(q  p)
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In 13 – 17, given that “p” is true, “q” is false, and “r” is true, determine the truth-value for each
13. p  q
14. ~(p
q)
15. (p
r)
q
16. q
17. (p  ~q) (~r  p)
r
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In 18 – 19, construct a truth table to determine the truth-value of
19. ( p  q)  p
18. ~p  ~q
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Classwork/Homework #3 (due Tues)
Conditional, Converse, Inverse, Contrapositive
In 1 – 4, for each given sentence: a) Identify the hypothesis “p” b) Identify the conclusion “q”
(Hint: You may have to re-write statement to form the conditional statement!)
1) If two lines are perpendicular, then they intersect.
2) When I finish my homework I will go to the movies
3) You can get to the stadium if you take the Third Avenue bus.
4) The perimeter of a square is 4s if the length of one side is s
In 5 – 8, Write the conditional and converse of a statement as a whole statement & in
symbolic form. If possible, give a counterexample of a false converse.
5) Given:
6) Given:
7) Given:
8) Given:
p: “An angle measures 90-degrees”
p: “x = 4”
p: “A quadrilateral has 4 right angles”
p: “Two angles are supplementary”
q: “It is a right angle”
q: “x2 = 16”
q: “It is a square”
q: “Their measure is 180-degrees.”
In 9 – 12, write the converse, inverse and contrapositive. Determine truth-value of each.
9) If x = 12, then x2 = 144.
10) If a figure is a square, then all of its angles are right angles.
11) If a number is odd, then it is divisible by three.
12) If M is the midpoint of AB , then AM  MB .
In 13 – 15, multiple-choice.
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13. Which statement is logically equivalent to “If it is Saturday, then I am not in school”?
(1) If I am not in school, then it is Saturday.
(3) If I am in school, then it is not Saturday.
(2) If it is not Saturday, then I am in school.
(4) If it is Saturday, then I am in school.
14. Which statement is the inverse of "If the waves are small, I do not go surfing"?
(1) If the waves are not small, I do not go surfing (3) If I go surfing, the waves are not small
(2) If I do not go surfing, the waves are small.
(4) If the waves are not small, I go surfing
15. What is the converse of the statement "If it is Sunday, then I do not go to school"?
(1) If I do not go to school, then it is Sunday.
(3) If I go to school, then it is not Sunday
(2) If it is not Sunday, then I do not go to school. (4) If it is not Sunday, then I go to school.
In 16 – 17, Construct a truth table
16. ~ q  ( p  q)
17. (p Λ q)  p
Homework/Classwork #4
BICONDITIONAL
In 1 – 2, Multiple Choice
1. Given the statement: "A right angle measures 90°." How is this statement written as a
biconditional?
(1) If an angle is a right angle, then it measures 90°.
(2) An angle is a right angle if, and only if, it measures 90°.
(3) An angle measures 90° and it is a right angle.
(4) If an angle does not measure 90°, then it is not a right angle.
2. Which statement is expressed as a biconditional?
(1) Two angles are congruent if they have the same measure.
(2) If two angles are both right angles, then they are congruent.
(3) Two angles are congruent if and only if they have the same measure.
(4) If two angles are congruent, then they are both right angles.
In 3 – 5 , Determine the truth-value of each bi-conditional statement.
3) 3y + 1 = 28 if and only if y = 9
4) An angle is an acute angle if and only if its degree measure is less than 90-degrees
5) I live in the United States if and only If I live in New York State
In 6 – 7 , write the converse. If the converse is true, write a true bi-conditional
6. p  q: If a triangle is isosceles, then it has two congruent sides.
7. pq: If you are 15 years old, then you are a teenager.
In 8 – 12, logic review
8. What is the converse of the statement “If it is 10. What is the inverse of the statement “If it is
sunny, I will go swimming”?
sunny, I will play baseball”?
(1) If it is not sunny, I will not go swimming.
(1) If I play baseball, then it is sunny.
(2) If I do not go swimming, then it is not sunny.
(2) If it is not sunny, I will not play baseball.
(3) If I go swimming, it is sunny.
(3) If I do not play baseball, then it is not sunny.
(4) I will go swimming if and only if it is sunny.
(4) I will play baseball if and only if it is sunny.
9. Which statement is logically equivalent to “If I 11. Given the true statement: “If a person is eligible
eat, then I live”?
to vote, then that person is a citizen.” Which
statement must also be true?
(1) If I live, then I eat.
(1) Kayla is not a citizen; therefore, she is not
(2) If I eat, then I do not live.
eligible to vote.
(3) I live if and only if I eat.
(2) Juan is a citizen; therefore, he is eligible to vote.
(4) If I do not live, then I do not eat.
(3) Marie is not eligible to vote; therefore, she is not
a citizen.
(4) Morgan has never voted; therefore, he is not a
citizen.