Logic Review

Multiple Choice
Identify the choice that best completes the statement or answers the question.

Make a conjecture about the next item in the sequence.

____	1.	
a.	1024	c.	4096	
b.	1025	d.	1022	

Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.

____	2.	Given:
Conjecture: 
a.	False; the angles are not vertical.	
b.	True	
c.	False; the angles are not complementary.	
d.	False; there is no indication of the measures of the angles.	

Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value.
p: An isosceles triangle has two congruent sides.	
q: A right angle measures 90º	
r: Four points are always coplanar.	
s: A decagon has 12 sides.	

____	3.	
a.	An isosceles triangle has two congruent sides and a right angle measures 90º; true.	
b.	An isosceles triangle has two congruent sides or a right angle measures 90º; true.	
c.	An isosceles triangle has two congruent sides or four points are always coplanar; true.	
d.	An isosceles triangle has two congruent sides or a right angle measures 90º; false.	

Short Answer

	4.	Write the statement All chickens have two wings in if-then form.

.

	5.	If you live in Michigan, then you live in Detroit.

Hypothesis:

Conclusion:

Inverse: 

Contrapositive:

Converse: 

.

	6.	In a group of 150 students, 60 students joined the math club, 54 students joined theater, and 27 students joined both. Draw a Venn diagram to represent the data.

.

7.	Use the truth table.

p	q	p Ù q	p Ú q	
T	T			
T	F			
F	T			
F	F			

Complete the truth table.

	8.	

	9.	Tell whether the statement is a biconditional.
a. I will work after school only if I have the time.

b. An angle is called a right angle if and only if it measures 90.

c. Two segments are congruent if and only if they have the same length.

10.	

	11.	Each of the following statements is true. Write the converse of each statement
and decide whether the converse is true or false. If the converse is true, combine
it with the original statement to form a true biconditional statement. If the
converse is false, state a counterexample.

a. If two points lie in a plane, then the line containing them lies in the plane.

b. If a number ends in 0, then the number is divisible by 5.

.

	12.	Rewrite the biconditional statement as a conditional statement and
its converse.
d. The ceiling fan runs if and only if the light switch is on.

e. You scored a touchdown if and only if the football crossed the goal line.

f. The expression 3x + 4 is equal to 10 if and only if x is 2