## Logical Connectivity

#### Logical Connectivity

Direction: Compound Statement:
Type 1: "If X then Y and Z"
This statement implies that:
(i) (X → Y and Z)
(ii) (~ Y or/and ~ Z → ~ X)
Type 2: "If X then Y or Z" or "Whenever X then Y or Z"
This statement implies that:
(i) (X → Y or Z)
(ii) (~ Y and ~ Z → ~ X)
(iii) X and ~ Y → Z)
(iv) X and ~ Z → Y)
Type 3: "Unless X , Y and Z" or "Either X or Y and Z"
This statement implies that:
(i) (~ X → Y or Z)
(ii) (~ Y or/and ~ Z → X)
Type 4: "Only if X then Y and Z"
This statement implies that:
(i) (Y and Z → X)
(ii) ( ~ X → ~ Y and/or ~ Z)
Each question consists of a main statement followed by 4 statements in the answer options. From the given options select the one that logically follow the main statement.

1. If Ricky singh is not at Pioneer Career then he is at his sleeping or watching movie.

1. This is the situation of "If X then Y or Z" it implies that:
(i) (X → Y or Z)
(ii) (~ Y and ~ Z → ~ X)
(iii) (X and ~ Z → Y)
(iv) (X and ~ Y → Z) given in option (A)

##### Correct Option: A

This is the situation of "If X then Y or Z" it implies that:
(i) (X → Y or Z)
(ii) (~ Y and ~ Z → ~ X)
(iii) (X and ~ Z → Y)
(iv) (X and ~ Y → Z) given in option (A)

1. Only if it is a national holiday, Pioneer career is not open and employee enjoy together.

1. This is the situation of "Only if X then Y and Z" it implies that:
(i) (Y and Z → X)
(ii) (~ X → ~ Y or/and ~ Z) given in option (C)

##### Correct Option: C

This is the situation of "Only if X then Y and Z" it implies that:
(i) (Y and Z → X)
(ii) (~ X → ~ Y or/and ~ Z) given in option (C)

1. If it is not raining then I will not walk slow but I will walk at least 4 km.

1. This is the situation of "If X then Y and Z" it implies that:
(i) (X → Y and Z)
(ii) (~ Y or/and ~ Z → ~ X ) given in option (C)

##### Correct Option: C

This is the situation of "If X then Y and Z" it implies that:
(i) (X → Y and Z)
(ii) (~ Y or/and ~ Z → ~ X ) given in option (C)

Direction: If all the three statements, marked (i), (ii) and (iii) are true, then which one of the following deductions, marked (1), (2), (3) and (4) can be MOST LOGICALLY deduced:

1. If a student sees a teacher in the class he would not sleep in the class, One day, a student does not see a teacher in the class. Which of the following statements is true?

1. Here let X be the event that the student sees a teacher. And event Y be the event that he is sleeping. We have been given that X → ~ Y. However, we do not know anything about ~ X, and the question asks us what Y will be if ~ X.
∴ We cannot conclude anything.

##### Correct Option: C

Here let X be the event that the student sees a teacher. And event Y be the event that he is sleeping. We have been given that X → ~ Y. However, we do not know anything about ~ X, and the question asks us what Y will be if ~ X.
∴ We cannot conclude anything.

Direction: Compound Statement:
Type 1: "If X then Y and Z"
This statement implies that:
(i) (X → Y and Z)
(ii) (~ Y or/and ~ Z → ~ X)
Type 2: "If X then Y or Z" or "Whenever X then Y or Z"
This statement implies that:
(i) (X → Y or Z)
(ii) (~ Y and ~ Z → ~ X)
(iii) X and ~ Y → Z)
(iv) X and ~ Z → Y)
Type 3: "Unless X , Y and Z" or "Either X or Y and Z"
This statement implies that:
(i) (~ X → Y or Z)
(ii) (~ Y or/and ~ Z → X)
Type 4: "Only if X then Y and Z"
This statement implies that:
(i) (Y and Z → X)
(ii) ( ~ X → ~ Y and/or ~ Z)
Each question consists of a main statement followed by 4 statements in the answer options. From the given options select the one that logically follow the main statement.

1. Unless students are agree, the class will continue and Institute will remain open.

1. This belongs to Type 3:- "Unless X, Y and Z" This statement implies that:
(i) (~ X → Y or Z)
(ii) (~ Y or/and ~ Z → X) Given in option (B)

##### Correct Option: B

This belongs to Type 3:- "Unless X, Y and Z" This statement implies that:
(i) (~ X → Y or Z)
(ii) (~ Y or/and ~ Z → X) Given in option (B)