Let's analyze the content of your image and solve the related questions. The problem involves sets and basic set theory operations.

Problem Details:

• Universal Set (U) = Whole numbers from 1 to 20.
• Set A = Multiples of 3.
• Set B = Factors of 16.

Given Questions:

(a) List the elements of set A.
(b) Is $A \subseteq B$? Justify.
(c) Is $B \subseteq A$? Justify.
(d) List the members of $A \cap B$ (Intersection of A and B).
(e) List the members of $A - B$ (Difference of A and B).
(f) Construct a Venn diagram for the Universal set, U.
(g) Determine the number of members in the complement of the set $A \cup B$.

Solution:

(a) List the elements of set A (Multiples of 3 in the range 1 to 20):

Multiples of 3 between 1 and 20 are: $A = \{3, 6, 9, 12, 15, 18\}$

(b) Is $A \subseteq B$? Justify:

To check if A is a subset of B, we need to know the elements of B.

(c) Is $B \subseteq A$? Justify:

We first need to find set B.

(d) List the members of $A \cap B$ (Intersection of A and B):

(e) List the members of $A - B$ (Difference of A and B):

(f) Construct a Venn diagram for the Universal set, U:

(g) Determine the number of members in the complement of the set $A \cup B$:

I will now calculate these values.Here are the results for the set operations:

(a) Elements of Set A (Multiples of 3 between 1 and 20):

$A = \{3, 6, 9, 12, 15, 18\}$

(b) Is $A \subseteq B$?

No, $A \subseteq B$ is False because none of the multiples of 3 are factors of 16.

(c) Is $B \subseteq A$?

No, $B \subseteq A$ is False because none of the factors of 16 are multiples of 3.

(d) Members of $A \cap B$ (Intersection of A and B):

The intersection is an empty set:
$A \cap B = \emptyset$

(e) Members of $A - B$ (Difference of A and B):

$A - B = \{3, 6, 9, 12, 15, 18\}$

(f) Venn Diagram: You can construct a Venn diagram with two circles representing sets A and B, showing that they do not overlap, since their intersection is empty.

(g) Number of members in the complement of $A \cup B$:

The complement of $A \cup B$ is:
$U - (A \cup B) = \{5, 7, 10, 11, 13, 14, 17, 19, 20\}$
There are 9 members in the complement.

Do you have any further questions or would you like additional details?

Follow-up Questions:

1. How do you calculate the union and complement of sets?
2. Can a Venn diagram have more than two sets?
3. What are the properties of subsets in general?
4. How is the difference of two sets computed?
5. What does an empty intersection signify in set theory?

Tip:

Always remember that $A \subseteq B$ means every element in $A$ must also be in $B$, and the same applies vice-versa for $B \subseteq A$.