Question

Question 1. Let A ith student got a perfect score on the first exam, for 1, ,19 a) Interpret (nA)using full sentences in plain English b) Interpret UA using full sentences in plain English, and argue that it is equivalent to (a) 442 19

Answer 1

a)

$\bigcap_{i=1}^{19}A_{i}$ would mean that all 19 students got a perfect score.

So, $(\bigcap_{i=1}^{19}A_{i})'$ means that none of the 19 students got a perfect score.

b)

$\bigcup_{i=1}^{19}A_{i}$ would mean that A₁ or A₂ or ......A₁₉ got a perfect score.

So, $\bigcup_{i=1}^{19}A_{i}'$ would include the events A₁ didn't get a perfect score or A₂ didn't get a perfect score or ......A₁₉ didn't get a perfect score i.e. none of the 19 students got a perfect score.

So, it is equivalent to (a).