Question

if a = 1 and b = -4 then prove that by using L.H.S and R.H.S

a^2. 2 ab. b^2
___ - ___ - ___ = a-b

a - b a - b a - b

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Answer 1

Step-by-step explanation:

We have x∈A, but x∉(B−C), thus x∈(A−B) and then we see that x∈(A−B)∪(A∩B∩C). And we have the LHS a subset of the RHS.

⇐

3 cases:

1.) x∈(A−B) only

from this we see that the RHS is a subset of the LHS

2.) x∈(A∩B∩C) only

This is not possible. Exclude this from our discussion.

3.) x∈(A−B)∧x∈(A∩B∩C)

This is not possible. Exclude this from our discussion.

Thus, the RHS is a subset of the LHS, shown by case 1.

Since the LHS is a subset of the RHS and the RHS is a subset of the LHS, then the LHS = RHS and

A−(B−C)=(A−B)∪(A∩B∩C)

Is this methodology right. I have more details in the proof I constructed but wanted to know if this method of thinking is good for the proof. Thanks!