click on the thumbnail ...I'm kinda not sure how to answer this as it's my first lesson
1(a) $A \setminus \{a,b,c\} = \{ \emptyset, \{ \emptyset \} , 1, \text{cat} , \{ 1, a, \text{cat} \} \}$
The $\setminus$ symbol means remove from the set. So, I look for the element $a$ in the set and remove it. The set containing $1, a, \text{cat}$ is not the same as the element $a$, so that whole set remains. Then, there are no elements $b,c$, so the rest of the set remains.
(b) That is the union operator. It will just add $x$ to the set.
(c) That is the intersection operator. You are looking for elements that are in both sets.
(d) That is the same operator from part (a). So, you want to remove the empty set. Note: the set containing the empty set will remain because the set containing the empty set is different from the empty set.
(e) This is similar to part (d) only the empty set will remain, but the set containing the empty set is removed.
(f) This is the symmetric difference operator. $A \Delta \{a,b,\{1,a,\text{cat}\}\} = \left( A\setminus \{a,b,\{1,a,\text{cat}\}\} \right) \cup \left( \{a,b,\{1,a,\text{cat}\}\} \setminus A\right)$
Thanks SlipEternal,
The way they explained it in the lecture was bit by bit and with really simple examples..then the lecturer gives us this to complete with symbols everywhere we just learnt which probably confused everyone like myself ,I was just staring at it thinking I have no idea what to do .
Legend
Cheers
do I just answer it like this ?
(a) is done by you
(b) can I just add x anywhere within the set .ie after the curly bracket after cat (or anywhere besides the sets already in the larger set containing all.
(c) just = cat
(d) just remove first empty set as you said and leave the rest
(e) remove the empty set from the set in the curly brackets
(f) I think ill do some research on that one as I don't know it well
Thanks a lot just for clarification cheers
so with (f) as is i did some research with the rule symmetric difference operator the empty sets become pretty much the same as in the original set and they are omitted .The resulting answer is just 1 of the elements in each set .The use of the A\-\A at the start to beginning of the answer in the set I'm not quite sure what that represents thanks