In boolean algebra, * (a dot, actually) and + are used for And and Or and the usual rules about association and commutation are used (PEMDAS, kinda, ommiting the * on occasion). Sometimes, what I might call, up arrow and down arrow are used, looking similar to ^ and v, in relation to set arithmetic symbols for the union and intersection oprators.

Another way to easily remember the arrows is to associate them with words: ^ with the A of and, and v with the V for vel (Latin for or). I always did this in logic class since I would always get confused otherwise.

I remembered these and union/intersection sign by imagining balls falling on the symbols from above - in case of V (OR) they would end up inside the symbol, which suggest summing/union, and in case of ^ (AND) they would get split and collect on opposite sides.

Also useful is making the arrows round-ended makes the the union/intersection signs, with or being union and and bring intersection (as it would be with the corresponding indicator functions).

Yes, it is.

But ^ and ∧ are different.

⊕ would be XOR using mathematical notation

The post is using boolean algebra symbols.

I used the notations found in FIPS 180-4 http://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.180-4.pdf