Discrete mathematics- beginner set problems

Question

A = {1, 2, 4, 5} B = {0, 2, 8} Considering the sets above are the following correct?

(A U B )\(A ∩ B) = {0, 1, 4, 5, 8}

(A\B) U (B\A) = {0, 1, 4, 5, 8}

(\A ∩ B ) U ( A ∩ \B) = {0, 1, 4, 5, 8}

Answer 1

Just work them out. Look up the meaning of "union" and "intersection" and understand what they mean. Then use this newfound understanding to compute the expressions on the left, and check they're the same as the ones on the right. Honestly, it's not rocket science.

If you want, you could even write a small Python script to compute the answers for you. Here's the commands you'll need. For example, the first expression would be (A | B) - (A & B) in Python syntax.

Answer 2

Just freaking do them!

$A\cup B = \{0, 1, 2, 4, 5, 8\} $ because that's what you get when you combine the elements together.

$A\cap B = \{2\}$ because those are all the elements the two sets have in common.

So $(A\cup B)\setminus (A\cap B)$ are all the elements of $\{0, 1, 2, 4, 5, 8\}$ that are not in $\{2\}$. And that is $\{0, 1, 4, 5, 8\}$ because this isn't brain science and any squid can follow directions.

...

Actually, the concept of $\setminus A$ may be unique. Is that supposed to mean the compliment of $A$? What is the implied universal set?