Given nonempty sets a and b, prove that every set in p(b − a) ⊆ p(b) − p(a).

Proof:

Let . As we chose in we know that . Since by transitivity we get:

.

If is the empty set, we already have that . But if is not empty, that means that it can't be subset of , because is already  subset of , and those sets do not share any element. In other words:

As can't be subset of , then . was an arbitrary element, and

Thus, , where we conclude that

answer: 1 and 3

step-by-step explanation:

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this