Download Name:_______________________________________________________ Date:________ Period:_______ Logic Regents Review

Name:_______________________________________________________ Date:________ Period:_______
Logic Regents Review
Negation:
1.) What are the truth values of the statement “Two is prime” and its negation?
(1) The statement is false and its negation is true.
(2) The statement is false and its negation is false.
(3) The statement is true and its negation is true.
(4) The statement is true and its negation is false.
2.) Given the statement:
One is a prime number.
What is the negation and the truth value of the negation?
(1) One is not a prime number; true.
(2) One is not a prime number; false.
(3) One is a composite number; true.
(4) One is a composite number; false.
3.) Write the negation of the statement “2 is a prime number,” and determine the truth value of the
negation.
4.) A student wrote the sentence “4 is an odd integer.” What is the negation of this sentence and the
truth value of the negation?
(1) 3 is an odd integer; true.
(2) 4 is not an odd integer; true.
(3) 4 is not an even integer; false.
(4) 4 is an even integer; false.
5.) Which statement is the negation of “Two is a prime number” and what is the truth value of the
negation?
(1) Two is not a prime number; false.
(2) Two is not a prime number; true.
(3) A prime number is two; false.
(4) A prime number is two; true.
6.) Given the true statement, “The medians of a triangle are concurrent,” write the negation of the
statement and give the truth value.
7.) What is the negation of the statement “I am not going to eat ice cream”?
(1) I like ice cream.
(2) I am going to eat ice cream.
(3) If I eat ice cream, then I like ice cream.
(4) If I don’t like ice cream, then I don’t eat ice cream.
8.) What is the negation of the statement “Squares are parallelograms”?
(1) Parallelograms are squares.
(2) Parallelograms are not squares.
(3) It is not the case that squares are parallelograms.
(4) It is not the case that parallelograms are squares.
Compound Statements:
1.) Which compound statement is true?
(1) A square has four sides or a hexagon has eight sides.
(2) A square has four sides and a hexagon has eight sides.
(3) If a square has four sides, then a hexagon has eight sides.
(4) A square has four sides if and only if a hexagon has eight sides.
2.) The statement “x is a multiple of 3, and x is an even integer” is true when x is equal to
(1) 9
(2) 8
(3) 3
(4) 6
3.) Which compound statement is true?
(1) A triangle has three sides and a quadrilateral has five sides.
(2) A triangle has three sides if and only if a quadrilateral has five sides.
(3) If a triangle has three sides, then a quadrilateral has five sides.
(4) A triangle has three sides or a quadrilateral has five sides.
4.) Given: Two is an even integer or three is an even integer.
Determine the truth value of this disjunction. Justify your answer.
Inverse, Converse, and Contrapositive:
1.) Which statement has the same truth value as the statement “If a quadrilateral is a square, then it
is a rectangle.”
(1) If a quadrilateral is a rectangle, then it is a square.
(2) If a quadrilateral is a rectangle, then it is not a square.
(3) If a quadrilateral is not a square, then it is not a rectangle.
(4) If a quadrilateral is not a rectangle, then it is not a square.
2.) Lines m and n are in plane A. What is the converse of the statement “If lines m and n are parallel,
then lines m and n do not intersect”?
(1) If lines m and n are not parallel, then lines m and n intersect.
(2) If lines m and n are not parallel, then lines m and n do not intersect.
(3) If lines m and n intersect, then lines m and n are not parallel.
(4) If lines m and n do not intersect, then lines m and n are parallel.
3.) What is the converse of “If an angle measures 90 degrees, then it is a right angle”?
(1) If an angle is a right angle, then it measures 90 degrees.
(2) An angle is a right angle if it measures 90 degrees.
(3) If an angle is not a right angle, then it does not measure 90 degrees.
(4) If an angle does not measure 90 degrees, then it is not a right angle.
4.) Consider the relationship between the two statements below.
If √16 + 9 ≠ 4, then 5 ≠ 4 + 3
If √16 + 9 = 4, then 5 = 4 + 3
These statements are
(1) inverses
(3) contrapositives
(2) converses
(4) biconditionals
5.) Which statement is logically equivalent to “If it is warm, then I go swimming”?
(1) If I go swimming, then it is warm.
(2) If it is warm, then I do not go swimming.
(3) If I do not go swimming, then it is not warm.
(4) If it is not warm, then I do not go swimming.
6.) What is the converse of the statement “If Bob does his homework, then George gets candy”?
(1) If George gets candy, then Bob does his homework.
(2) Bob does his homework if and only if George gets candy.
(3) If George does not get candy, then Bob does do his homework.
(4) If Bob does not do his homework, then George does not get candy.
7.) What is the inverse of the statement “If two triangles are not similar, their corresponding angles
are not congruent”?
(1) If two triangles are similar, their corresponding angles are not congruent.
(2) If corresponding angles of two triangles are not congruent, the triangles
are not similar.
(3) If two triangles are similar, their corresponding angles are congruent.
(4) If corresponding angles of two triangles are congruent, the triangles are similar.
8.) What is the contrapositive of the statement, “If I am tall, then I will bump my head”?
(1) If I bump my head, then I am tall.
(2) If I do not bump my head, then I am tall.
(3) If I am tall, then I will not bump my head.
(4) If I do not bump my head, then I am not tall.
Make sure you know the definitions, notes, symbols, and truth table values for:
 Negation
 Conjunction
 Disjunction
 Conditional
 Biconditional
Make sure you know the definitions, notes, and truth values for:
 Converse
 Inverse
 Contrapositive
Answer Key to the above questions: