Mba-day6 logic - hypothetical reasoning exercises

Hypothetical formula

Exercises

Example 1

As long as there is no fog , The plane can take off on time , Which of the following correctly expresses the above conclusion ：

• i If the plane takes off on time , There must be no fog
• ii If the plane doesn't take off on time , There must be fog
• iii Unless it's foggy , Otherwise the plane will take off on time

 Explain ：“ as long as ... Just ” It belongs to the sufficient condition in the hypothesis , namely p->q  and   Not q-> Not p, Is not  （ If p, that q） = p  And not q, So only the following is true ：
p->q: As long as there is no fog , The plane can take off on time 
 Not q-> Not p: The plane didn't take off on time , It's foggy 
“ Unless p,  otherwise q"  Equivalent to   If the p be q  Equivalent to   If it doesn't fog , Take off on time 

 That is, only ii and iii correct 

Example 2

Xiao Zhang promised ： If it doesn't rain , I must go to the concert , Which of the following is true , It shows that Xiao Zhang has not fulfilled his promise ？

• i It didn't rain , Xiao Zhang didn't go to the concert
• ii It's raining , Xiao Zhang went to the concert
• iii It's raining , Xiao Zhang didn't go to the concert

 Explain ：“ If ... Just ” A sufficient condition for a false statement , namely p->q  and   Not q-> Not p, Is not  （ If p, that q） = p  And not q, So only the following is true ：
1. p->q：  No rain , Then you must go to the concert 
2.  Not q-> Not p： Don't listen to the concert , Then it rains 

 Xiao Zhang didn't keep his promise , It shows that the test is not a formula , That is not  （ If p, that q）= p  And not q =  No rain , You don't go to the concert 

 The correct option is ：i

Example 3

As long as there is （ Enough courage and wisdom ）, Just ( Nothing is impossible ), If the above conclusion is true , Which of the following must be true ？

• A If something can't be done , It shows that they lack enough courage , And lack enough wisdom .
• B If something can't be done , Shows a lack of courage , Or lack enough wisdom

 Explain ：“ as long as ... Just ” A sufficient condition for a false statement , namely p->q  and   Not q-> Not p, Is not  （ If p, that q） = p  And not q, So only the following is true ：
p->q： As long as you have enough courage and wisdom , There's nothing that can't be done 
 Not q-> Not p： What didn't happen , There is no courage or wisdom 

 Correct selection ：B

Example 4

As long as the diagnosis and treatment are accurate and the rescue is timely , Then the patient will not die . Now the patient is unfortunately dead . If the above conclusion is true , Which of the following is not necessarily true ？

• A The diagnosis and treatment of this patient is not accurate , Rescue is not timely
• B The diagnosis and treatment of this patient is not accurate , But the rescue was timely
• C The patient was not rescued in time , But the diagnosis and treatment is not accurate
• D If the cause of the patient's death is inaccurate diagnosis and treatment , Then the untimely rescue will not be the reason
• E If the diagnosis and treatment of this patient is accurate , Then the reason for his death is that the rescue must not be in time .

 Explain ：“ as long as ... Just ” A sufficient condition for a false statement , namely p->q  and   Not q-> Not p, Is not  （ If p, that q） = p  And not q, So only the following is true ：
p->q:  as long as ( Accurate diagnosis and treatment and timely rescue ), that （ This patient will not die ）
 Not q-> Not p：（ The patient will die ）, The diagnosis and treatment is not accurate or the rescue is not timely 

 In the title stem, now the patient unfortunately died , It can be inferred that the diagnosis and treatment is not accurate or the rescue is not timely 
 If the diagnosis and treatment are not accurate or the rescue is not conducted in time, the relationship between or , There are the following 2 Maybe 
 Inaccurate diagnosis and treatment , Rescue in time  
 Accurate diagnosis and treatment , The rescue is not timely  

 So check the options , Only E That's right. 

Example 5

If （ If both a and B fail the exam ）, that ( C must have passed ). What options need to be added , You can pass the exam .

 Explain ：“ If ... that ” A sufficient condition for a false statement , Use non q-> Not p
 If C fails , A passes or B passes 
 Further , C must fail , B failed , Can 100% Get a pass in the exam