How to Efficiently Handle Set Operations Without Inbuilt Functions?

[chwala]

Homework Statement

This is my original question; Given $A=[1,2,x,y]$ $B=[2,x,z,m]$ $C=[4,5]$, then find
$A-(BUC)$

Relevant Equations

set theory

ok we shall have $(A-B)∩(A-C)= [1,y]∩[1,2,x,y]=[1,y]$ correct?

 

[WWGD]

Have you heard of DeMorgan's laws?

 

[FactChecker]

Homework Statement:: This is my original question; Given $A=[1,2,x,y]$ $B=[2,x,z,m]$ $C=[4,5]$, then find
$A-(BUC)$
Relevant Equations:: set theory

ok we shall have $(A-B)∩(A-C)= [1,y]∩[1,2,x,y]=[1,y]$ correct?

Correct. But it concerns me that you seem unable to check your answers yourself. That is a skill that is just as important to learn as anything else.

 

[chwala]

Have you heard of DeMorgan's laws?

Yes that's what I used...$M-(B∪Q)=(M-B)∩(M-Q)$

 

[chwala]

Correct. But it concerns me that you seem unable to check your answers yourself. That is a skill that is just as important to learn as anything else.

I am able to check...I ask because I may want a different perspective from what I know...I am always learning...cheers

 

[PeroK]

I am able to check...I ask because I may want a different perspective from what I know...I am always learning...cheers

My perspective would be that if you want a simple answer to this, you do the following:

a) Write down the elements of the set $A$: $1, 2, x, y$.

b) Write down the elements of $B \cup C$: $2, x, z, m, 4, 5$

c) Go through the set $B \cup C$ one element at a time and delete these elements from the list in set $A$.

1d) That gives the answer $A - (B \cup C) = \{1, y\}$

If you want to verify De Morgan's law by using this as an example, then fine. But, don't lose sight of the simple fact that $A - (B \cup C)$ means things that are in $A$ with anything that is in either $B$ or $C$ removed.

 

[WWGD]

Yes, it's a good think not to rely only on big formulas , but what if you have similar with a large collection of sets? It becomes a nightmare to do a specific example.

 

[PeroK]

Yes, it's a good think not to rely only on big formulas , but what if you have similar with a large collection of sets? It becomes a nightmare to do a specific example.

If I were coding this, without using inbuilt set operations, then I would do it either the way described; or, not bother with the union at all, but just go through $B$ and $C$ separately and delete elements from $A$. My first step wouldn't be the form the sets $A - B$ and $A - C$.

For example, pseudocode for $X = A - (B_1 \cup B_2 \dots \cup B_n)$:

Create set $X = A$
For $k = 1$ to $n$:
Remove any element in $B_k$ from $X$
(or, $X = X - B_k$ for short)
Loop
Print $X$