Math Is Fun Forum

ross.s

Member

Registered: 2011-07-31

Posts: 1

Struggling with Set Identities

Hi everyone,
I am doing discrete math this semester & am currently working on set identities. I have worked through some examples & seem to be able to figure most out, however the following one has me stumped

Use the set property A-B=A n B' to show that for all sets A,B and C  (n=intersection, U = union)
A-(B U C) = (A-B) n (A-C)

So I m starting with the RHS of equation, as it is more complex and want to simplify it

(A-B) n (A-C)
(A n B') n (A n C')

I'm stuck here.......any suggestions?

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Struggling with Set Identities

hi ross.s

welcome to the forum!hope you like it here.

you can do this using the definitions of union intersection difference and complement of a set.

example:
x∈(A U B) if and only if x∈A or x∈B.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Struggling with Set Identities

now you can substitute p=x∈A q=x∈B and r=x∈C and solve this as a tautology.

Last edited by anonimnystefy (2011-07-31 03:29:43)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.