Exam 1

1. Metainformation

   Tag	Value
   file	Probability_uva-events-760-en_uva-events-760-en
   name	uva-events-760-en
   section	Probability/Elementary Probability/Events
   type	schoice
   solution	TRUE, FALSE, FALSE, FALSE
   Type	Conceptual
   Language	English
   Level	Statistical Literacy
   IRT-Difficulty	2.598
   p-value	0.4549

   Question

   $\begin{aligned} A & = \left \{ x \mid x = 2k, k \in Z \right \}\\ B & = \left \{ x \mid x = 2k + 1, k \in Z \right \}\\ C & = \left \{ x \mid x = 2(k + 1), k \in Z \right \}\\ D & = \left \{ x \mid x = 2k - 1, k \in Z \right \} \end{aligned}$

   where Z is the set of all the integers (positive and negative) numbers, including 0. If each time two sets make a cross section then which one yields an empty set?

   
   
   1. TRUE: $A \cap B = \varnothing, A \cap C = \varnothing, C \cap B = \varnothing, C \cap D = \varnothing$
   2. FALSE: $A \cap D = \varnothing, A \cap C = \varnothing, C \cap B = \varnothing, C \cap D = \varnothing$
   3. FALSE: $A \cap B = \varnothing, A \cap C = \varnothing, B \cap D = \varnothing, C \cap B = \varnothing$
   4. FALSE: $A \cap B = \varnothing, A \cap D = \varnothing, C \cap B = \varnothing, C \cap D = \varnothing$
   
   
   1. $A \cap B = \varnothing, A \cap C = \varnothing, C \cap B = \varnothing, C \cap D = \varnothing$: Correct
   2. $A \cap D = \varnothing, A \cap C = \varnothing, C \cap B = \varnothing, C \cap D = \varnothing$: Incorrect
   3. $A \cap B = \varnothing, A \cap C = \varnothing, B \cap D = \varnothing, C \cap B = \varnothing$: Incorrect
   4. $A \cap B = \varnothing, A \cap D = \varnothing, C \cap B = \varnothing, C \cap D = \varnothing$: Incorrect