damn college is a waste of time
sorry i dont speak english
Well, I don't know what any of that means (didn't need to learn that yet I guess), so I can't give you an answer.
i may be saying a bunch of dumb things and everything may be wrong but:
first one, symmetric difference and intersection:
- union | A /s\ B + A /i\ B
- complementar | (A /s\ B + A /i\ B) /s\ U
second, symmetric difference and union:
- intersection | (A u B) - (A /s\ B)
- complementar | U - (A u B)
third, complementar and symmetric difference:
- union | A /s\ B + \(A /s\ B)
- intersection | (A /s\ B + \(A /s\ B)) - A /s\ B
last one, union and intersection:
- complementar | U - A u B
note: i am not sure if I understood the problem correctly, and also the proofs (at least on my head) are all visual and hard to share on HLTV, but they are actually quite simple (assuming im right)
symbols: BIG U to universe, /s\ to symmetric difference, /i\ to intersection and little u for union
Also, I just skipped the ones where I could use the symbol to define itself
ive never seen a question that says "Justify your answer rigorously"
Fucking hate abstract algebra
imagine having high IQ and solve useless problem ...
Honestly don't even know what am I looking at
Let's say N is intersection, D is delta, U is union and \ is \
1. A U B = (A D B) D (A N B)
A N B = A N B
A \ B = (A D B) D (B D (A N B)
2. A U B = A U B
A N B = (A U B) D (A D B)
A \ B = (A U B) D B
3. A U B = ((A D B) \ B) D B
A N B = A \ (A D B)
A \ B = A \ B
4. A U B = A U B
A N B = A N B
A \ B = A N B'
You just want someone to do your homework for you?
let me roll my joint, i will explain it step by step after
what is \ and delta, I've only seen union (U) and intersection (upside-down U)