Use the properties of sets to prove that for all the sets A and B
A – (A∩B) = A – B

Question

Use the properties of sets to prove that for all the sets A and B
A – (A∩B) = A – B

goformit100 · Answer

@satellite73 Sir Help Me Please.

mathslover · Answer

I think, drawing venn diagram for it will work.

mathslover · Answer

Use De Morgan's law : 

$A - (B \cap C ) = (A-B) \cup (A-C) $ 

We have : $A - (A \cap B) = (A-A) \cup (A-B) $

$0 \cup (A-B) = A-B $

mathslover · Answer

Not zero, $\phi \cup (A-B) = A-B$

mathslover · Answer

Got it? @goformit100

goformit100 · Answer

ok

anonymous · Answer

Given 2 sets $\bf A=\left\{ 1,2,3 \right\}$ and $\bf B=\left\{ 2,3,4 \right\}$, we find that:$$\bf A ∩ B =\left\{ 1,2,3 \right\} ∩\left\{ 2,3,4 \right\}=\left\{ 2,3 \right\}$$$$\bf A-(A∩B)=\left\{ 1,2,3 \right\}-\left\{ 2,3 \right\}=\left\{ 1 \right\}$$$$\bf A-B=\left\{ 1,2,3 \right\}-\left\{ 2,3,4 \right\}=\left\{ 1 \right\}$$This concludes that:$$\bf A-(A∩B)=A-B$$But we must prove this equality for any general case for two given sets A and B for which you can do what mathslover stated.