For each of the following draw a Venn diagram for sets A, B, and C that satisfies the given conditions:
a. Draw a Venn diagram for sets A, B, and C such that A⊆B;C⊆B;A and C have no elements in common
b. Draw a Venn diagram for sets A, B, and C such that C⊆A: B and C have no elements in common
To draw a Venn diagram for sets A, B, and C that satisfy the given conditions, follow these steps:
a. A ⊆ B; C ⊆ B; A and C have no elements in common:
1. Start by drawing three overlapping circles to represent sets A, B, and C.
2. Since A ⊆ B, the circle representing B should be larger than the circle representing A, so that all elements of A are also in B.
3. Next, add the circle representing C inside the circle representing B, as C ⊆ B.
4. Finally, make sure the circles representing A and C do not overlap, indicating that A and C have no elements in common.
b. C ⊆ A; B and C have no elements in common:
1. Similarly, start by drawing three overlapping circles to represent sets A, B, and C.
2. Since C ⊆ A, the circle representing A should be larger than the circle representing C, so that all elements of C are also in A.
3. Add the circle representing B in a position that does not overlap with the circle representing C, indicating that B and C have no elements in common.
4. Finally, ensure that the circle representing C is fully contained within the circle representing A to represent the subset relationship between the two sets.
Remember, the purpose of a Venn diagram is to visually represent the relationships between sets and their elements. The specific size and position of the circles may vary as long as they accurately convey the given conditions.