IST 230 SOLUTIONs to Chapter 2.1 Homework
 pp. 85–87, #
15,
24,
30,
33,
42,
46,
52,
54,
66,
77,
80

Let the universe be the set U = { 1, 2, 3, ..., 10 }.
Let A = { 1, 4, 7, 10 }, B = { 1, 2, 3, 4 , 5 }, and C = { 2, 4, 6, 8 }.
List the elements.
Set:
¬ ( A B )
C

Draw a Venn diagram and shade the given set.
Set:
( B – ¬ C ) ( ( B – ¬ A )
( C
B ) )

A television poll of 151 persons found that
68 watched "Law and Disorder";
61 watched "The East Wing";
52 watched "The Tenors" ;
16 watched both "Law and Disorder" and "The East Wing" ;
25 watched both "Law and Disorder" and "The Tenors";
19 watched both "The East Wing" and "The Tenors"; and
26 watched none of these shows.
How many watched all three show?

Let X = { 1, 2 } and Y = { a, b, c }.
List the elements in the set.
Set:
Y x X
 List all partitions of the set.
Set: { a, b, c }

Answer true or false.
{ x } Î { x, { x } }

Determine whether the pair of sets is equal.
Pair of Sets:
{ x  x is a real number and 0 < x £ 2 }, { 1, 2 }

List the members Ã ( { a, b, c, d } ).
Which are proper subsets of { a, b, c, d }?

Determine if the statement is true, otherwise give a counterexample.
The sets X, Y, and Z are subsets of the universal set U.
Assume that the universe for cartesian products is U x U.
Statment:
¬ ( X x Y ) = ¬ X x ¬ Y for all sets X and Y

The symmetric difference of two sets A and B is the set
A D B = ( A B ) – ( A
B ).
Given a universe U, describe A D A, U
D A, and Æ
D A.

Find a formula for A B
C  similar to the formula of Exercise 79.
Show that your formula holds for all sets A, B, and C.
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