Discrete Mathematics - Basic Set Theory : Assignment review : Q1

[Supierreious]

Question 1 :
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Homework Statement

Consider the following sets, where U represents a universal set :

U = {1, 2, 3, 4, ∅, {1}}
A = {1, 3}
B = {{1}, 1}
C = {2 , 4}
D = { ∅ , 1, 2 }

Homework Equations

Choose the correct option : D - B is the set :

1. {∅,2}
2. {∅}
3. {2}
4. ∅

The Attempt at a Solution

So the question refers to one set, minus another set. Having a look at the 2 sets in question :
D - B :

{ ∅ , 1, 2 } - {{1}, 1}

I see that set B does, which needs to be subtracted from set D, contains elements that are in set D, and elements that are not in set D. According to my understanding, only values that are in set D, can be deducted from set D. In this case the value in set B, that can be deducted from set D, is '1'. There are no other sets that can be deducted.

Thus, if we build the new set, it will look like the below :

D - B = { ∅ , 2 }

So in looking at my solution to this problem, the correct answer is number 1.


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Please review and let me know if my understanding in this question , as well as my answer is correct. I am spending some extra time in ensuring my answers are correct, for my assignments.


Thanks!

 

[QED Andrew]

Both your understanding and answer are correct. Cheers. :)