Question

For any three sets a b and c prove that a-(b-c)=

Answer 1

hlo mate i have found this for ur question maybe this is correct

Prove that for all sets A, B, and C, (A - B) - C = (A - C) - (B-C)

Just follow the definition.We define:
A−B={x∈U;x∈A∧x∉B}A−B={x∈U;x∈A∧x∉B}
Thus write left side of the equation:

(A−B)−C={x∈U;x∈(A−B)∧x∉C}(A−B)−C={x∈U;x∈(A−B)∧x∉C}={x∈U;x∈A∧x∉B∧x∉C}={x∈U;x∈A∧x∉B∧x∉C}

Now let's write the right side:

(A−C)−(B−C)=(A−C)−(B−C)= 
{x∈U;x∈(A−C)∧x∉(B−C)}={x∈U;x∈(A−C)∧x∉(B−C)}=
{x∈U;(x∈A∧x∉C){x∈U;(x∈A∧x∉C)∧(x∉B∧x∉C)}=∧(x∉B∧x∉C)}=
={x∈U;x∈A∧x∉B∧x∉C}={x∈U;x∈A∧x∉B∧x∉C}

When you compare these two sets, they are the same. Q.E.D.