Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Discrete mathematics, continuous mathematics, and probability (resit) / 1 / d / i

Table of contents
- Solution i

Solution

For every set

S

, the definition of a power set gives

S \in P (A \cap B) ⟺ S \subseteq A \cap B ⟺ (S \subseteq A and S \subseteq B) ⟺ S \in P (A) \cap P (B) .

Equality by identical membership therefore proves

P (A \cap B) = P (A) \cap P (B) .

The essential observation is that being a subset of a set intersection means being a subset of both factors.

 Ancestors (12)

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version