Name: ______________________________________________________________ Date:__________________ Period:______
Chapter 12: Logic
Topic #3: Related Conditional Statements
Remember:
The conditional is a statement that uses "if... then." The only time a conditional is false is if the hypothesis is
true and the conclusion is false.
The three related conditional statements are the __________________, ______________, and __________________.
Converse:
The ________________of a conditional statement is formed by _________________hypothesis and the conclusion. The
parts of the sentences __________________places but the "If... then" do not move.
Example:
Conditional: If the space shuttle is launched, then a cloud of smoke was seen.
Converse: _______________________________________________________________
______________________________________________________________________________
Inverse:
The ________________of a conditional statement is formed by ________________both the hypothesis and the
conclusion. In other words, the word "___________" is added to both parts of the conditional statement.
Example:
Conditional: If you grew up in Alaska, then you have seen snow.
Inverse: _______________________________________________________________
______________________________________________________________________________
Contrapositive:
The __________________of a conditional statement is formed by ___________________the hypothesis and conclusion
and by ___________________the resulting negations. In other words, the contrapositive both "________________" and
"________________" the original statement. Basically, we are combining the ________________and the ________________.
Conditional: If I am hungry, then I will eat a peanut.
Contrapositive: ___________________________________________________________
______________________________________________________________________________
The __________________always has the same value as the __________________. When two statements always have the
same truth value, they are said to be ________________________.
Examples:
1. Which of the following statement is the converse of "If the moon is full, then vampires are prowling"?
(1) If vampires are prowling, then the moon is full.
(2) If the moon is not full, then vampires are not prowling.
(3) If vampires are not prowling, then the moon is not full.
2. Which of the following statement is logically equivalent to "If you live in a mansion, then you have a high
heating bill"?
(1) If you have a high heating bill, then you live in a mansion.
(2) If you do not have a high heating bill, then you do not live in a mansion.
(3) If you do not live in a mansion, then you do not have a high heating bill.
3.) Consider the relationship of the two statements below.
If 22 ≠ 5, then 5 + 6 ≠ 11.
If 5 + 6 ≠ 11, then 22 ≠ 5
These statements are
(1) inverses
(3) contrapositives
(2) converses
(4) biconditionals
4.) Which statement is logically equivalent to "If it is summer, then I am at the beach"?
(1) If it is not summer, then I am not at the beach.
(2) If I am at the beach, then it is summer.
(3) If I am not at the beach, then it is summer.
(4) If I am not at the beach, then it is not summer.
5.) Which statement is the inverse of "If it is July, then we do not have school"?
(1) If it is not July, then we do have school.
(2) If it is not July, then we do not have school.
(3) If we do not have school, then it is July.
(4) If we have school, then it is not July.
6.) Which statement has the same truth value as "If a square has four sides, then it is not a hexagon."
(1) If a square is not a hexagon, then it has four sides.
(2) If a square does not have four sides, then it is a hexagon.
(3) If a square is a hexagon, then it does has four sides.
(4) If a square is a hexagon, then it does not have four sides.
7.) Consider the relationship between the two statements below:
If 2 + 3 = 5, then 2 + 3 ≠ 6.
If 2 + 3 ≠ 5, then 2 + 3 = 6.
These statements are
(1) inverses
(3) converses
(2) contrapositives
(4) biconditionals
Name: ______________________________________________________________
Date:__________________Period:______
Related Conditional Statements Homework
Complete the questions below. Circle your answer for multiple choice questions.
1.) Which statement is logically equivalent to “If I am in a mathematics class, then I am having fun”?
(1) If I am not in a mathematics class, then I am not having fun.
(2) If I am having fun, then I am in a mathematics class.
(3) If I am not having fun, then I am not in a mathematics class.
(4) If I am in a mathematics class, then I am not having fun.
2.) What is the converse of the statement “If a2 + b2 = c2, then ΔABC is a right triangle”?
(1) If ΔABC is a right triangle, then a2 + b2 = c2.
(2) a2 + b2 = c2 if and only if ΔABC is a right triangle.
(3) If ΔABC is not a right triangle, then a2 + b2 ≠ c2.
(4) If a2 + b2 = c2, then ΔABC is not a right triangle.
3.) Which statement is logically equivalent to “If I sleep, then I will not eat”?
(1) If I do not sleep, then I will eat.
(2) If I eat, then I will not sleep.
(3) If I eat, then I will sleep.
(4) If I do not eat, then I will sleep.
4.) What is the inverse of the statement “If x is an even integer, then (x + 1) is an odd integer”?
(1) x is not an even integer if and only if (x + 1) is not an odd integer.
(2) x is an even integer if and only if (x + 1) is an odd integer.
(3) If (x + 1) is an odd integer, then x is an even integer.
(4) If x is not an even integer, then (x + 1) is not an odd integer.
5.) Write a statement that is logically equivalent to “If 4 is an even integer, then it is divisible by 2”. What is
that statement called?
Review Questions:
6.) In the accompanying diagram, figure B is the image of figure A. Which type of transformation was
performed?
(1) dilation
(2) translation
(3) rotation
(4) reflection
7.) Which transformation is illustrated by the accompanying diagram?
(1) translation
(2) reflection
(3) rotation
(4) dilation
8.) Angle A and angle B are complementary angles. If m<A = x, which expression represents the number of
degrees in angle B?
(1) x – 180
(2) 180 – x
(3) x – 90
(4) 90 – x
9.) Point (-2,3) is reflected in the x-axis. In which quadrant does its image lie?
(1) I
(2) II
(3) III
(4) IV
10.) Which is not a property of similar triangle?
(1) The corresponding angles are congruent.
(2) The corresponding sides are congruent.
(3) The perimeters are in the same ratio as the corresponding sides.
(4) The altitudes are in the same ratio as the corresponding sides.