# True / False Sets

• Nov 4th 2008, 12:38 PM
captainjapan
True / False Sets
TRUE or FALSE. Assume that the statement applies to all sets.

a)
A -(B -C) = (A -B) C
FALSE

b)
(A -C) -(B -C) = A B
TRUE

c)
A U (B C) = (A U B) (A U C)
TRUE

d)
A (B U C) = (A U B) (A U C)
FALSE

e)
(A U B) U A = A
????

f)
If A B = A U B, then A = B.
???

Thanks
• Nov 4th 2008, 01:27 PM
poutsos.B
Quote:

Originally Posted by captainjapan
TRUE or FALSE. Assume that the statement applies to all sets.

a)
A -(B -C) = (A -B) C
FALSE

b)
(A -C) -(B -C) = A B
TRUE

c)
A U (B C) = (A U B) (A U C)
TRUE

d)
A (B U C) = (A U B) (A U C)
FALSE

e)
(A U B) U A = A
????

f)
If A B = A U B, then A = B.
???

Thanks

f) IS true here is a proof:

assume AUB = A\$\displaystyle \cap\$ B.

Assume xεA ====> xεA v xεΒ <====> xε(ΑUB) ====> xε(A\$\displaystyle \cap\$ B) (Since AUB = A\$\displaystyle \cap\$ B.) and xε(A\$\displaystyle \cap\$ B)=====> xεA & xεB ====> xεB.

Hence .... A is a subset of B .In the same way we prove B is a subset of A

e) is also true here is a proof:

(AUB')' U A' = (A'\$\displaystyle \cap\$ B)UA' = (A' \$\displaystyle \cap\$ T)U(A'\$\displaystyle \cap\$ B) =

A'\$\displaystyle \cap\$(TUB) = A' \$\displaystyle \cap\$ T = A'

SINCE :
A' \$\displaystyle \cap\$ T=A' and BUT=T WHERE T is for true