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Exercise 2.4.4: Set operations, part 2.

Sets A through H are defined as follows.

• A = {1, 2, 3, 4}
• B = {-1, -2, -3}
• C = {-1, 0, 1, 2, 3}
• D = {2, 3, 4, 5, 6, 7}
• E = {x Z: x is odd}
• F = {x Z⁺: x 7}
• G = {x Z⁺: x < 7}
• H = {x Z⁺: x 6}

Indicate whether each statement is true or false.

(g)

C

(h)

{{0}} P(C)

(i)

C F = C G

(j)

E F R

(k)

P(B)

Exercise 2.5.3: Showing set equations that are not identities.

A set equation is not an identity if there are examples for the variables denoting the sets that cause the equation to be false. For example A B = A B is not an identity because if A = {1, 2} and B = {1}, then A B = {1, 2} and A B = {1}, which means that A B A B.

Show that each set equation given below is not a set identity.

(c)

(A B) - (A B) = A - B

(d)

(B - A) A = A

(e)

A B = A B

Exercise 2.6.2: Cartesian product of two small sets.

Define the sets X and Y as: X = {*, +, $} and Y = {52, 67}. Use the definitions for X and Y to answer the questions.

(b)

Give an element of X⁴. Express your answer as a 4-tuple, not as a string.

(c)

Give an element of X X Y Y X. Express your answer as a 5-tuple, not as a string.