Answer:

1.Originally Answered: What are the subset of {1,2,3}? ... What is the maximum number of elements in B if B is proper subset of C and number of subsets in C is 8?

A subset is a collection of members of the set or the set itself is a subset of the set

Total number of elements is 3. So the subset will be {1} {2} {3} { 1 2 } { 1 3 } {2 3 }

This set has only three elements. Subsets can be of the following categories in terms of number ...

Try every possible combination. Let me start: {}, {1}, {2}, {3}… It might get interesting ...

Total number of subsets are =2^3 =8 {1} {2} {3} { 1 2 } { 1 3 } {2 3 } { 1 2 3 } and { } ...

2.Including all four elements, there are 24 = 16 subsets. 15 of those subsets are proper, 1 subset, namely {a,b,c,d}, is not.

3.Example 2: Given X = {a, r, e} and Y = {r, e, a, d}, what is the relationship between these sets? We say that X is a subset of Y, since every element of X is also in Y.

4.Subset: A set A is a subset of a set B if every element of A is also an element of B.

Notation: A ⊆ B is read, “Set A is a subset of set B.”

Example: For A = {red, blue} and B = {red, white, blue}, A ⊆ B since every element of A is also an element of B.

Example: The set {a, b, c} has 8 subsets.