Question
PLEASE TYPE ONLY*** Exercise 2.4.4: Set operations, part 2. Sets A through H are defined as follows. A = {1, 2, 3, 4} B =
PLEASE TYPE ONLY***
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.
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