To assist with your homework, here are the solutions to a few selected questions from the document you uploaded:

1. Write down all possible subsets of the set {1,2}.

The set {1,2} has 4 possible subsets, which are:

• ∅ (empty set)
• {1}
• {2}
• {1,2}

3. Write the number of proper subsets of a set having six elements.

The total number of subsets of a set with $n$ elements is $2^n$. For $n = 6$, the total number of subsets is: $2^6 = 64$ The number of proper subsets is always 1 less than the total number of subsets (since the set itself is not included in proper subsets), so the number of proper subsets is: $64 - 1 = 63$

10. Find the domain and range of the function $f(x) = \frac{1}{x-1}$.

• Domain: The function $f(x) = \frac{1}{x-1}$ is undefined when $x = 1$ because division by zero is not allowed. Hence, the domain is all real numbers except $x = 1$, which is: $\text{Domain} = (-\infty, 1) \cup (1, \infty)$
• Range: The function can take any real value except 0, because the function approaches zero but never actually reaches it. Therefore, the range is: $\text{Range} = (-\infty, 0) \cup (0, \infty)$

16. A and B are two sets such that $n(A) = 3$ and $n(B) = 6$. Find:

1. Minimum value of $n(A \cup B)$: The minimum value occurs when all elements of A are also in B. In this case, $n(A \cup B) = n(B) = 6$.
2. Maximum value of $n(A \cap B)$: The maximum value occurs when A and B have no common elements. In this case, $n(A \cup B) = n(A) + n(B) = 3 + 6 = 9$.

18. If $B \subseteq A$, show that $(C - B) \subseteq (C - A)$.

• Since $B \subseteq A$, every element of $B$ is also an element of $A$. Therefore, any element that is in $C - B$ (i.e., in $C$ but not in $B$) will also be in $C - A$ because $A$ contains $B$. Thus, $C - B \subseteq C - A$.

Would you like details on any specific problem or more clarification?

Here are 5 related questions:

1. How many subsets would a set with 5 elements have?
2. What is the difference between proper subsets and improper subsets?
3. Can you find the range of the function $f(x) = \frac{1}{x^2 - 4}$?
4. What are the subsets of the set {a, b, {c}}?
5. What is the minimum value of $n(A \cup B)$ if $n(A) = 4$ and $n(B) = 5$?

Tip: Always remember that a set with $n$ elements has $2^n$ total subsets, including both proper and improper ones!