Question

Monitor three consecutive packets going through a Internet router. Based on the packet header, each packet can be classified as either video ( v ) if it was sent from a YouTube server or as ordinary data ( d ). Your observation is a sequence of three-letters (each letter is either v or d ). For example, two video packets followed by one data packet corresponds to vvd . Write the elements of the following sets:
A 1 = { second packet is video } ,
B 1 = { second packet is data } ,
A 2 = { all packets are the same } ,
B 2 = { video and data alternate } ,
A 3 = { one or more video packets } ,
B 3 = { two or more data packets } .
For each pair of events A 1 and B 1 , A 2 and B 2 , and so on, identify whether the pair of events is either mutually exclusive or collectively exhaustive or both.

Answer 1

Recall that Ai and Bi are collectively exhaustive if Ai [ Bi = S. Also, Ai and Bi are mutually exclusive if Ai\Bi = . Since we have written down each pair Ai and Bi above, we can simply check for these properties.
The pair A1 and B1 are mutually exclusive and collectively exhaustive. The pair A2 and B2 are mutually exclusive but not collectively exhaustive. The pair A3 and B3 are not mutually exclusive since dvd belongs to A3 and B3. However, A3 and B3 are collectively exhaustive.