#### MarkFL

##### Super Moderator
Staff member
Here are what the various symbols mean:

$$\displaystyle \in$$ is an element of

$$\displaystyle \subset$$ is a proper subset of

$$\displaystyle \not\in$$ is not an element of

$$\displaystyle \not\subset$$ is not a proper subset of

Do you understand how to determine if a given element is an element of a set, or if one set is the proper subset of another set?

• topsquark

#### MarkFL

##### Super Moderator
Staff member

a) $$\displaystyle 12\in A$$

We see that 12 in deed listed as an element of set $$A$$, so this is true.

b) $$\displaystyle 14\not\in B$$

We see that 14 is not given as an element of set $$B$$, so this is true.

c) $$\displaystyle 14\not\in B$$

We see that 13 is given as an element of set $$B$$, so this is false.

d) $$\displaystyle \{10,16\}\subset A$$

We see that both 10 and 16 are elements of set $$A$$ and that set $$A$$ has elements other than these two, and so this is true.

e) $$\displaystyle A\not\subset B$$

We see that there are elements in set $$A$$ that are not in set $$B$$, and so this is true.

f) $$\displaystyle B\subset A$$

We see that all elements of set $$B$$ are also in set $$A$$ and that there are elements in set $$A$$ that are not in set $$B$$ and so this is true.