Deck 6: Set Theory

Question 1

Answer 1

20

Question 2

Consider the statement
Complete the proof begun below in which the given statement is derived algebraically from
the properties listed in Theorem 6.2.2. Be sure to give a reason for every step that exactly
justifies what was done in the step:
which is the right-hand side of the equation to be shown. [Hence the given statement is true.]
(The number of lines in the outline shown above works for one version of a proof. If you write
a proof using more or fewer lines, be sure to follow the given format, supplying a reason for
every step that exactly justifies what was done in the step.)

Answer 2

Question 3

Disprove the following statement by finding a counterexample.

Answer 3

Question 4

Derive the following result "algebraically" using the properties listed in Theorem 6.2.2. Give
a reason for every step that exactly justifies what was done in the step.

Question 5

Question 6

Write a negation for the following statement:

Question 7

Justify your answers carefully. (In other words, provide a proof if the statement is true or a
disproof if the statement is false.)

Question 8

Derive the following result. You may do so either "algebraically" using the properties listed in
Theorem 6.2.2, being sure to give a reason for every step, or you may use the element method
for proving a set equals the empty set.

Question 9

Question 10

Consider the statement
The proof below is the beginning of a proof using the element method for proving that the
set equals the empty set. Complete the proof without using any of the set properties from
Theorem 6.2.2.

Question 11

Is the following sentence a statement: This sentence is false or
Justify your answer.

Question 12

Question 13

Question 14

Let A and B be sets. Define precisely (but concisely) what it means for A to be a subset of B.

Question 15

Question 16

Use the element method for proving a set equals the empty set to prove that

Question 17

Justify your answers carefully. (In other words, provide a proof if the statement is true or a
disproof if the statement is false.)

Question 18

Fill in the blanks:

Question 19

Prove the following statement using an element argument and reasoning directly from the
definitions of union, intersection, set difference.