Let U = {x|x ≤ 25, x ∈ N}, A = {x|x ≤ 12, x ∈ N}, B = {x|9 ≤ x ≤ 18, x ∈ N}.
Answer the following four questions using the above information.
Find A'
1 point
{13, 14, 15, 16, 17, ..., 25}
{1, 2, 3, ..., 8, 13, 14, 15, ..., 25}
{1, 2, 3, ..., 8, 19, 20, 21, ..., 25}
Find B′.
1 point
{13, 14, 15, 16, 17, ..., 25}
{1, 2, 3, ..., 8, 13, 14, 15, ..., 25}
{1, 2, 3, ..., 8, 19, 20, 21, ..., 25}
Find (A ∩ B)′.
1 point
{1, 2, 3, ..., 8, 19, 20, 21, ..., 25}
{1, 2, 3, ..., 8, 13, 14, 15, ..., 25}
{13, 14, 15, 16, 17, ..., 25}
Find A′ ∪ B′.
1 point
{1, 2, 3, ..., 8, 13, 14, 15, ..., 25}
{13, 14, 15, 16, 17, ..., 25}
{1, 2, 3, ..., 8, 19, 20, 21, ..., 25}
Find A – B.
1 point
{1, 2, 3, ..., 8}
{13, 14, 15, 16, 17, ..., 25}
{13, 14, 15, ..., 25}
Using the Venn diagram, list the elements of the following sets:
(A ∪ B) – C *
1 point
{1, 3, 5, 7}
{11, 13}
{19, 21}
{15, 17, 19, 21}
(B ∩ C) – A *
1 point
{1, 3, 5, 7}
{11, 13}
{19, 21}
{15, 17, 19, 21}
A′ ∩ B *
1 point
{1, 3, 5, 7}
{11, 13}
{19, 21}
{15, 17, 19, 21}
C′ – A *
1 point
{1, 3, 5, 7}
{11, 13}
{19, 21}
{15, 17, 19, 21}
A′ ∪ B′ *
0 points
{1, 3, 5, 7}
{11, 13}
{19, 21}
{15, 17, 19, 21}
Answers
Answer:
In Section 2.1, we used logical operators (conjunction, disjunction, negation) to form new statements from existing statements. In a similar manner, there are several ways to create new sets from sets that have already been defined. In fact, we will form these new sets using the logical operators of conjunction (and), disjunction (or), and negation (not). For example, if the universal set is the set of natural numbers N and
A={1,2,3,4,5,6} and B={1,3,5,7,9},(5.1.1)
The set consisting of all natural numbers that are in A and are in B is the set {1,3,5} ;
The set consisting of all natural numbers that are in A or are in B is the set {1,2,3,4,5,6,7,9} ; and
The set consisting of all natural numbers that are in A and are not in B is the set {2,4,6}.
These sets are examples of some of the most common set operations, which are given in the following definitions