algebraic laws of sets

**may** · May 25th 2010, 11:45 PM

Excuse me,how to do this type of question?

Using the laws of the algebra of sets show that

(a-b)∩(a∩b)'=a∩b'

**Deadstar** · May 26th 2010, 05:00 AM

$(A \backslash B) \cap (A \cap B)'$

$= (A \cap B') \cap (A' \cup B')$

$= A \cap B' \cap (B' \cup A')$

$= A \cap B'$

Where we used the following rules...

$(A \backslash B) = (A \cap B')$

$(A \cap B)' = (A' \cup B')$

$B' \cap (B' \cup A') = B'$

**Wilmer** · May 26th 2010, 05:01 AM

laws of the algebra of sets - Google Search=

**Grandad** · May 26th 2010, 06:43 AM

Hello everyone

All that Deadstar says is correct, but I think the statement

$B' \cap(B'\cup A') = B'$

(although obvious) requires further proof - it's not one of the usual Set Laws (although some people do include it as an Absorption Law).

You prove it like this:

$B' \cap(B'\cup A') = (B' \cup \oslash)\cap(B'\cup A')$

$=B'\cup(\oslash \cap A')$

$=B'\cup\oslash$

$=B'$

Grandad

**may** · May 26th 2010, 06:45 AM

$(A \backslash B) = (A \cap B')$

$(A \cap B)' = (A' \cup B')$

$B' \cap (B' \cup A') = B'$ [/quote]

how to know when to apply this rule?

**Grandad** · May 26th 2010, 06:48 AM

Hello may

Originally Posted by may

Where we used the following rules...

$(A \backslash B) = (A \cap B')$

$(A \cap B)' = (A' \cup B')$

$B' \cap (B' \cup A') = B'$

how to know when to apply this rule?

Sorry - there's no quick answer to that - just lots of practice!

Grandad

**may** · May 26th 2010, 06:56 AM

Originally Posted by Grandad

Hello everyone

All that Deadstar says is correct, but I think the statement

$B' \cap(B'\cup A') = B'$

(although obvious) requires further proof - it's not one of the usual Set Laws (although some people do include it as an Absorption Law).

You prove it like this:

$B' \cap(B'\cup A') = (B' \cup \oslash)\cap(B'\cup A')$

$=B'\cup(\oslash \cap A')$

$=B'\cup\oslash$

$=B'$

Grandad

which formula Grandad are using to change fr

[/SIZE][INDENT] $B' \cap(B'\cup A') = (B' \cup \oslash)\cap(B'\cup A')$
[INDENT] $=B'\cup(\oslash \cap A')$

$=B'\cup\oslash$ [SIZE=3]

**may** · May 26th 2010, 06:59 AM

Originally Posted by Grandad

Hello maySorry - there's no quick answer to that - just lots of practice!

Grandad

HOW to do this type of question?Must we memorise All the formula?

**Grandad** · May 26th 2010, 07:05 AM

Hello may

Originally Posted by may

which formula grandad are using to change fr
$B' \cap(B'\cup A') = (B' \cup \oslash)\cap(B'\cup A')$

$=B'\cup(\oslash \cap A')$

This uses the Distributive Law:

$(P \cup Q)\cap (P \cup R) = P \cup (Q \cap R)$

where I have replaced $P$ by $B'$ , $Q$ by $\oslash$ and $R$ by $A'$ .

Originally Posted by may

HOW to do this type of question?Must we memorise All the formula?

Yes, I'm rather afraid that you do. As I said - you'll need lots of practice!

Grandad

PS ... and to answer your extra question, following your edit:

$\oslash \cap A' = \oslash$ uses what I have always known as an Identity Law, but others sometimes refer to as a Domination Law.

See, for example, here.

**may** · May 27th 2010, 08:11 AM

Originally Posted by Grandad

Hello mayThis uses the Distributive Law:

$(P \cup Q)\cap (P \cup R) = P \cup (Q \cap R)$

where I have replaced $P$ by $B'$ , $Q$ by $\oslash$ and $R$ by $A'$ .

Yes, I'm rather afraid that you do. As I said - you'll need lots of practice!

Grandad

PS ... and to answer your extra question, following your edit:

$\oslash \cap A' = \oslash$ uses what I have always known as an Identity Law, but others sometimes refer to as a Domination Law.

See, for example, here.

Oh,thanks Grandad at last i start to figure out how to do this type of question.thank you very much

**may** · May 27th 2010, 08:22 AM

Originally Posted by Grandad

Hello mayThis uses the Distributive Law:

$(P \cup Q)\cap (P \cup R) = P \cup (Q \cap R)$

where I have replaced $P$ by $B'$ , $Q$ by $\oslash$ and $R$ by $A'$ .

Yes, I'm rather afraid that you do. As I said - you'll need lots of practice!

Grandad

PS ... and to answer your extra question, following your edit:

$\oslash \cap A' = \oslash$ uses what I have always known as an Identity Law, but others sometimes refer to as a Domination Law.

See, for example, here.

Oh,thanks Grandad at last i start to figure out how to do this type of question.thank you very much

erm i want to ask another question..same topic do i need to put the question in new thread or at here?

**Grandad** · May 27th 2010, 01:31 PM

Hello may

Originally Posted by may

Oh,thanks Grandad at last i start to figure out how to do this type of question.thank you very much

erm i want to ask another question..same topic do i need to put the question in new thread or at here?

Start a new thread.

Grandad

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