Here are the solutions to the remaining problems on your worksheet. I have worked through each one step-by-step to ensure they are correct.
10. Complement of even numbers (1–100)
*
The Set: The problem gives the set $\{2, 4, 6, 8, ... 100\}$. These are all the
even numbers between 1 and 100.
*
The Universe: Integers from 1 through 100.
*
The Complement: The complement is everything in the universe that is *not* in the set. If we take away all the even numbers, we are left with all the
odd numbers.
*
Answer: The set of odd integers from 1 through 99: $\{1, 3, 5, ..., 99\}$
11. Complement of odd numbers (1–27)
*
The Set: The problem gives $\{1, 3, 5, 7, ... 27\}$. These are all the
odd numbers between 1 and 27.
*
The Universe: Integers from 1 through 27.
*
The Complement: We need the numbers from 1 to 27 that are *not* odd. These are the
even numbers.
*
Answer: $\{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26\}$
12. Intersection of A and B
* $A = \{-5, -4, 0, 4, 5\}$
* $B = \{-6, -5, 0, 5, 6\}$
*
Intersection ($\cap$): Look for numbers that appear in
both lists.
* $-5$ is in both.
* $0$ is in both.
* $5$ is in both.
*
Answer: $\{-5, 0, 5\}$
13. Union of A and B (from #12)
*
Union ($\cup$): Combine every number from both lists into one big list. Do not repeat numbers if they appear twice.
* List A: $-5, -4, 0, 4, 5$
* List B: $-6, -5, 0, 5, 6$
* Combined: $-6, -5, -4, 0, 4, 5, 6$
*
Answer: $\{-6, -5, -4, 0, 4, 5, 6\}$
14. Intersection of new A and B
* $A = \{-500, -12, -1, 1, 5, 57\}$
* $B = \{-12, -1, 1, 5, 22\}$
*
Intersection ($\cap$): Find the matches.
* $-12$ is in both.
* $-1$ is in both.
* $1$ is in both.
* $5$ is in both.
* ($-500$ and $57$ are only in A; $22$ is only in B).
*
Answer: $\{-12, -1, 1, 5\}$
15. Union of new A and B
*
Union ($\cup$): Combine all unique numbers from both lists.
* From A: $-500, -12, -1, 1, 5, 57$
* From B: $22$ (the others are already listed)
* Combined order: $-500, -12, -1, 1, 5, 22, 57$
*
Answer: $\{-500, -12, -1, 1, 5, 22, 57\}$
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Final Answer:
10. $\{1, 3, 5, ..., 99\}$ (The set of odd integers from 1 to 99)
11. $\{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26\}$
12. $\{-5, 0, 5\}$
13. $\{-6, -5, -4, 0, 4, 5, 6\}$
14. $\{-12, -1, 1, 5\}$
15. $\{-500, -12, -1, 1, 5, 22, 57\}$
Parent Tip: Review the logic above to help your child master the concept of set theory worksheet.
