Thread: 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

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 B.

Assume xεA ====> xεA v xεΒ <====> xε(ΑUB) ====> xε(A B) (Since AUB = A B.) and xε(A 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' B)UA' = (A' T)U(A' B) =


A' (TUB) = A' T = A'

SINCE :
A' T=A' and BUT=T WHERE T is for true