TheGreat
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Could someone help me in this by simplifying/Proving the equation using Theorems/ Rules on Operation of Sets (i.e Commutative property, idempotent, assoc, dist. , definition of union , def. intersection , DeMorgan ,etc.).
Letting A, B and C be three sets ..
Prove/Disprove :
View attachment 5616
Any solution would be much of help. Hoping to get answers .. Do help me :) Thank you!
I've seen similar questions in here like this:
Problem posted: Prove/Disprove : A−(B∩C) = (A−B)∩(A−C)
Thank you once again ... Hoping I could get some answer also ..
- jer
Letting A, B and C be three sets ..
Prove/Disprove :
View attachment 5616
Any solution would be much of help. Hoping to get answers .. Do help me :) Thank you!
I've seen similar questions in here like this:
Problem posted: Prove/Disprove : A−(B∩C) = (A−B)∩(A−C)
soroban said:Hello, KOO!
We should work on one side of the equation.
\begin{array}{cccccc}<br /> 1. & A -(B \cap C) && 1. &\text{Given} \\<br /> 2. & A \cap(B\cup C)^c && 2. &\text{def. Subtr'n} \\<br /> 3. & A \cap B^c \cap C^c && 3. & \text{DeMorgan} \\<br /> 4. & A \cap A \cap B^c \cap C^c && 4. & \text{Duplication} \\<br /> 5. & A\cap B^c \cap A \cap C^c && 5. & \text{Commutative} \\<br /> 6. & (A \cap B^c) \cap (A \cap C^c) && 6. & \text{Associative} \\<br /> 7. & (A-B) \cap (A-C) && 7. & \text{def. Subtr'n}\end{array}
Thank you once again ... Hoping I could get some answer also ..
- jer
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