Let's say you have 2 sets, A and B. If A ⊂ B, it means that ALL the elements of set A are also found in set B.

For example, if set A = {1, 2, 3} and set B = {1, 2, 3, 4}. A ⊂ B, since all the elements of C are found in D. Conversely, B ⊃ A, meaning that B is a superset of A. That means B contains all the elements of A, and then some more.

Let's say you have 2 other sets, C and D. If C is not a subset of D (also written as C ⊄ D), then one or more of set C's elements are not in D.

For example, if set C = {1, 3, 5} and D = {3, 5, 6}, then C ⊄ D.

How many subsets can you have for a given set?

where n(A) is the number of elements of set A. For example, if a given set Z = {0, 1}, then,

Note that an empty is also a subset of pretty much every set, including itself.

E.g.

Given that A = {2, 3, 4, 5} and B = {x : x is an integer and 1 ≤ x ≤ 8}.

(a) By using the symbol ⊂, write a relation between A and B.

(b) Draw a Venn diagram to represent the relationship between the two sets.

(a) A ⊂ B

(b)

The Venn diagram shows four sets P, Q, R and S. Write a relation between

(a) P and Q,

(b) Q and S,

(c) S and R,

(d) Q and R,

(e) P and P

(a) P ⊂ Q

(b) Q ⊂ S

(c) R ⊂ S

(d) Q ⊂ R

(e) P ⊂ P (since all elements of P are in P)

The universal set is usually represented by the symbol U.

Given that the universal set U = {x : 1 ≤ x ≤ 9, x is an integer},

A = {numbers that are a multiple of 3}, and

B = {factors of 8}.

(a) List all the elements of set A and set B

(b) Draw a Venn diagram to represent the relationship between U, A, and B.

(a) A = {3, 6, 9}, B = {1, 2, 4, 8}

(b)

The universal set contains all elements in both the shaded and unshaded area. Set A is the unshaded circle, while its complement, set A' (read as A prime), is represented by the shaded area.

Given that universal set U = {factors of 100}, A = {perfect squares}, and B = {two-digit numbers}.

(a) List the elements of A' and B'.

(b) Draw a Venn diagram to represent (i) A' and U, (ii) B' and U.

U = {1, 2, 4, 5, 10, 20, 25, 50, 100}

(a)

A = {1, 4, 25, 100}

A' = {2, 5, 10, 20, 50}

B = {10, 20, 25, 50}

B' = {1, 2, 4, 5, 100}

(bi)

(bii)

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Damien: By definition, the complement of a given set A refers to the set of elements outside A.
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Damien: Do you have a sample problem you're having problems with? Maybe show what you've done so far?

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**Mom Teacher** Not rated yet

Why is an empty set a subset of a set?
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My solution: …

**I still cant understand....** Not rated yet

I just cant understand what subset is.
Damien: Let's say you have the complete "set" of the "Lord of the Rings" DVD collection (that is, DVDs 1, 2 and …