(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Question 1 :

a) Use Venn diagrams to determine whether or not, for all subnets A,B and C of a universal set U, (A-B) ∪ C = (A∪C) - (A∩B)

b) If the statement appears to hold, give a proof, if not, give a counter example.

2. Relevant equations

(A-B) ∪ C = (A∪C) - (A∩B)

*there are no other variables given

*no other values are known

*this question relates to the proof

3. The attempt at a solution

a) I have drawn the Venn diagrams, which does not reflect that they equate to each other, so they are not equal.

b) The counter example is the one I am struggling with, so i will explain how i did it, and basically just adapted an answer from my text book :

Attempt to prove with counter example :

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Let : A = {1;2}

Let : B = {2;3}

Let : C = {1;4}

Left hand : (A-B) ∪ C :

(A-B) = = {1;2} - {2;3} = {1;3}

(A-B) ∪ C = {1;3} ∪ C = {1;3} ∪ {1;4} = {1;3;4}

(A-B) ∪ C = {1;3;4}

Now to find out what the right hand side is :

(A∪C) - (A∩B) :

(A∪C) = {1;2}∪{1;4} = {1;2;4}

(A∩B) = {1;2}∩{2;3} = {2}

(A∪C) - (A∩B) = {1;4}

Thus :

(A-B) ∪ C ≠ (A∪C) - (A∩B)

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Please let me know if this is right, or where i can improve, this is something new to me, and i still need to work on this alot.

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# Homework Help: Discrete Mathematics : Proof : Question 1

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