## Logical Connectivity

#### Logical Connectivity

1. If Rajesh studies, he will pass his exam. Rajesh fails the exam. Which one of the following can be concluded from the above statements?
1. Rajesh studied for the exam
2. Rajesh did not study for the exam
3. Rajesh may or may not have studied for the exam (No definite conclusion)
4. None of these

1. Let X the event that Rajesh studies for the exam. and Y the event that Rajesh passes the exam. We have been given the information that X → Y.
Thus ~ Y ~X. means if Ram failed the exam, he did not study for it.

##### Correct Option: B

Let X the event that Rajesh studies for the exam. and Y the event that Rajesh passes the exam. We have been given the information that X → Y.
Thus ~ Y ~X. means if Ram failed the exam, he did not study for it.

1. Whenever I go in sun I feel headache, which one of the following can be concluded from this?
1. I went in sun so I have headache now.
2. I didn't go in sun so I don't have headache now.
3. I m feeling headache that means I went in sun.
4. None of these

1. The given statement is: Whenever I go in sun I feel headache. Here let us assume that X is "I go in sun" and Y is "I have headache"
Then situation is "Whenever X then Y" and implications in this is (X → Y) and (~ Y → → X), now lets check options one by one
Option (a) I went in sun so I have headache now. (X → Y) its right conclusion.
Option (b) I didn't go in sun so I don't have headache now.(~ X → Y) it can not be concluded
Option (c) I m feeling headache that means I went in sun. (Y → X), it can not be concluded.

##### Correct Option: A

The given statement is: Whenever I go in sun I feel headache. Here let us assume that X is "I go in sun" and Y is "I have headache"
Then situation is "Whenever X then Y" and implications in this is (X → Y) and (~ Y → → X), now lets check options one by one
Option (a) I went in sun so I have headache now. (X → Y) its right conclusion.
Option (b) I didn't go in sun so I don't have headache now.(~ X → Y) it can not be concluded
Option (c) I m feeling headache that means I went in sun. (Y → X), it can not be concluded.

1. Ram will either buy a Car or a Flat which one of the following can be concluded from this?
1. Ram bought a Flat so he will not buy a car.
2. Ram bought a Car so he will not buy a Flat.
3. Ram did not bought Car so he must have bought Flat.
4. None of these

1. It is the case of "Either X or Y" hence (~ X → Y) and (~ Y → X) hence option (C) is correct.

##### Correct Option: C

It is the case of "Either X or Y" hence (~ X → Y) and (~ Y → X) hence option (C) is correct.

Direction: In each of the following sentences, the main statement is followed by four sentences each. Select a pair of sentences that relate logically to the given statement.

1. The teacher gives a break, only if students are exhausted.
(i) The teacher gives break
(ii) The teacher did not give a break
(iii) Students are not exhausted
(iv) Students are exhausted
1. (i) and (iii)
2. (i) and (iv)
3. (ii) and (iv)
4. None of these

1. The conclusion can be: The teacher gives break means Students are exhausted (as given in i and iv) Students are not exhausted hence teacher will not give a break (as given in ii and iii)

##### Correct Option: B

The conclusion can be: The teacher gives break means Students are exhausted (as given in i and iv) Students are not exhausted hence teacher will not give a break (as given in ii and iii)

1. Either CAT is tough or IIT JEE is easy
(i) CAT is tough
(ii) CAT is Easy
(iii) IIT JEE is easy
(iv) IIT JEE is tough.
1. (ii) and (iii)
2. (ii) and (iv)
3. (iii) and (iv)
4. None of these

1. This is the case of either X or Y the conclusion should be:
CAT is not tough (means Easy) then IIT JEE is Easy [as given in ii and iii)
IIT JEE is tough then CAT is tough [ as given in iv and i]

##### Correct Option: A

This is the case of either X or Y the conclusion should be:
CAT is not tough (means Easy) then IIT JEE is Easy [as given in ii and iii)
IIT JEE is tough then CAT is tough [ as given in iv and i]