AI-ADVANCED LEARNER

 

1.

If P represents 'This book is good' and Q represents 'This book is cheap', write the following sentences in symbolic form:

(a) This book is good and cheap.

(b) This book is not good but cheap.

(c) This book is costly but good.

(d) This book is neither good nor cheap.

(e) This book is either good or cheap.

 

2.

Translate the following sentences into propositional forms:

(a) If it is not raining and I have the time. then I will go to a movie.

(b) It is raining and I will not go to a movie.

(c) It is not raining.

(d) I will not go to a movie.

(e) I will go to a movie only if it is not raining.

Hints:

 Let P be the proposition 'It is raining'.

Let Q be the proposition 'I have the time'.

Let R be the proposition '1 will go to a movie'.

 

3.

Write the following sentences in symbolic form: (

a) This book is interesting but the exercises are difficult.

(b) This book is interesting but the subject is difficult.

(c) This book is not interesting. the exercises are difficult but the subject is not difficult.

(d) If this book is interesting and the exercises are not difficult then the subject is not difficult.

(e) This book is interesting means that the subject is not difficult, and conversely.

(f) The subject is not difficult but this book is interesting and the exercises are difficult.

(g) The subject is not difficult but the exercises are difficult.

(h) Either the book is interesting or the subject is difficult.

 

 

4.

Derive S from the following premises using a valid argument:

(i)                  P => Q

(ii)                Q => ¬R

(iii)               P v S

(iv)               R

 

5.

Check the validity of the following argument:

If Ram has completed B.E. (Computer Science) or MBA, then he is assured of a good job.

 If Ram is assured of a good job, he is happy.

Ram is not happy.

So Ram has not completed MBA.

 

6.

Express the following sentences involving predicates in symbolic form:

1. All students are clever.

2. Some students are not successful.

3. Every clever student is successful.

4. There are some successful students who are not clever.

5. Some students are clever and successful.

7.

Discuss the validity of the following argument:

All educated persons are well behaved.

Ram is educated.

No well-behaved person is quarrelsome.

Therefore. Ram is not quarrelsome.

8.

Test the validity of the following argument:

Babies are illogical.

Nobody is despised who can manage a crocodile.

Illogical persons are despised.

Therefore babies cannot manage crocodiles.

 

9.

Show that the following argument is valid:

All men are mortal.

Socrates is a man.

So Socrates is mortal.

 

10.

Test the validity of the following argument:

If Ram is clever then Prem is well-behaved.

If Joe is good then Sam is bad and Prem is not well-behaved.

If Lal is educated then Joe is good or Ram is clever.

Hence if Lal is educated and Prem is not well-behaved then Sam is bad.