GATE Mechanical 2016 Set 2 | GA | Question: 4

Question

Fact: If it rains, then the field is wet.
Read the following statements:

1. It rains
2. The field is not wet
3. The field is wet
4. It did not rain

Which one of the options given below is NOT logically possible, based on the given fact?

• A. If $(iii)$, then $(iv)$.
• B. If $(i)$, then $(iii)$.
• C. If $(i)$, then $(ii)$.
• D. If $(ii)$, then $(iv)$.

Answer 1

Option B and D are not the answer due to the fact that question asks about which of the given option NOT logically possible .
Option B is given fact, and option D is contrapositive of given fact.

Option A, field may be wet but that does not mean there is a rain. So this logically possible.

Option C, it is logically not possible, if it rains then field must be wet. Thus option C is only correct option.

Comments

A statement is a logical statement if it is either True or False but never both.

Option A can also be the answer because the statement ‘If the field is wet then it did not rain’ may be True or False.

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@Anand patel bro the question is asking which option is NOT logically possible , 

Since the option A is logically possible that’s why it is not the correct answer . 

Answer 2

C is the answer,

A is Logically possible as If the field is wet, Then It may or maynot rained....

B is the given statement...

and C is also Logically possible If the Field is not wet,Then definately there is no rain ...

Answer 3

Both A. And C should be correct

Answer 4

If it rains then the field is wet ---> if p then q

from this we can derive solutions such as 

case 1 p->q a case of unique solution
case 2 ~p->q or ~p->~q , hence a case of not unique solution  but solution exists neverthless
case 3 q->p or q->~q same solution exists but not a unique solution 
case 4 ~q->~p is again a case of unqiue solution

option a) If (iii), then (iv). is q->~p which is a possible solution as we can see by case 3 
option b) If (i), then (iii). is p->q which represents the unique solution from case 1
option c ) If (i), then (ii). is p->~q this as we can see from the above cases cant be logically derived
option d) If (ii), then (iv) is ~q->~p which represents the unique solution from case 4

Hence (c) is the only correct option.