0
$\begingroup$

Due to my little knowledge in set theory, I simply don't know how the authors of Statistical Inference could make this highlighted statement enter image description here

Could someone please explain? What book should I read to have a better understanding of these type out-of-the-blue statements? Thanks.

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ Draw the Venn diagram: that will make it obvious. $\endgroup$
    – whuber ♦
    Commented Nov 18, 2019 at 17:31
  • $\begingroup$ Thanks, @whuber. The authors warned against using Venn diagrams as they were not rigorous. I know it's difficult sometime without visualisation, but I feel that might bring my thinking and reasoning ability to higher level. $\endgroup$
    – Nemo
    Commented Nov 19, 2019 at 0:08
  • 1
    $\begingroup$ Venn diagrams are perfectly rigorous when correctly drawn. Regardless, they can provide the insight you need as well as suggest rigorous algebraic demonstrations. Insight is gained by using multiple tools and approaches, not by eschewing any technique. $\endgroup$
    – whuber ♦
    Commented Nov 19, 2019 at 13:53

1 Answer 1

Reset to default
2
$\begingroup$

It reads like this: Elements in $B$ consist of elements that are either in $A$ or $A^c$ (i.e. not in $A$). So, elements in both $A$ and $B$ fall in the set $A\cap B$, and elements in $B$ but not in $A$ fall in $B\cap A^c$. This is the all possible situations for elements in $B$.

Improve this answer
$\endgroup$
2
  • $\begingroup$ Another great answer, @gunes! Was it your own logical reasoning or from established concepts/axioms? Could you please recommend a book that I should read to obtain these fundamental concepts from? Thanks. $\endgroup$
    – Nemo
    Commented Nov 18, 2019 at 23:56
  • 1
    $\begingroup$ I believe you can review Elementary Set Theory from Doris. $\endgroup$
    – gunes
    Commented Nov 19, 2019 at 6:28

Not the answer you're looking for? Browse other questions tagged or ask your own question.