Chapter 1.7, Problem 13PSC

a

To determine

To Show: The statements given are true is to be proved

Explanation of Solution

Given information: The following statements have been given

• Spoof is a set of all purrs
• Spoof contains at least two different distinct purrs
• Every lilt is a set of purrs and contains at least two distinct purrs
• If A and B are two any distinct purrs, there is one and only one lilt that contains them
• No lilt contains all the purrs

Proof: The following statements are to be proven

Statement i : There is at least one lilt

• From the above statements, if purrs exist, then lilt will exist

Hence, the statement is proved to be true

Statement ii : There are at least three purrs

• Using the given statement “No lilt contains all the purrs”, we can say that lilts have to be more than one
• Using the given statement “If A and B are two any distinct purrs, there is one and only one lilt that contains them”, we can say that there are at least two purrs in one lilt
• Using our both previous arguments, we can say that that there are at least three purrs

  Hence, the statement is proved to be true

Statement iii : There are at least three lilts

• Using the given statement “No lilt contains all the purrs”, we can say that lilts have to be more than one
• Using the given statement “If A and B are two any distinct purrs, there is one and only one lilt that contains them”, we can say that lilts have to be more than two

  Hence, the statement is proved to be true

b

To determine

To Find: The stated case has to be found where the lilts girt and mirt are not same

Answer to Problem 13PSC

The found condition is that pil and til are the only two purrs

Explanation of Solution

Given information: The information can be decoded from the given statements

  $girt\in (pil,til)$

  $mirt\in (pil,til)$

Calculation: we use the following statement

• Using the given statement “If A and B are two any distinct purrs, there is one and only one lilt that contains them”, we can say that only one of girt or mirt can contain these two elements unless these are the only two purrs present

Hence, the found condition is that pil and til are the only two purrs