Question Details

A Main Statement is followed by four Statements labelled P , Q, R and S. Choose the ordered pair of the Statements where the first Statement implies the second, and the two Statements are logically consistent with the Main Statement.

Main Statement: Pradeep becomes either a Director or a Producer.

Statement P: Pradeep is a Director.
Statement Q: Pradeep is a Producer.
Statement R: Pradeep is not a Director.
Statement S: Pradeep is not a Producer.
Select the correct answer.

Options

SP only

RQ only

Both SP and RQ

Neither SP nor RQ

Show Answer

Correct Answer :

Option C

Both SP and RQ

Solution :

The correct option is Both SP and RQ.

Understanding the Main Statement:
The main statement is: "Pradeep becomes either a Director or a Producer."
In standard logical reasoning, a statement of the form "Either A or B" (disjunction) means that at least one of the two conditions must be true. If one of the conditions is false, the other condition must be true to satisfy the statement. Let us analyze the given statements:
P: Pradeep is a Director.
Q: Pradeep is a Producer.
R: Pradeep is not a Director (Not P).
S: Pradeep is not a Producer (Not Q).

Analyzing the Ordered Pairs:
An ordered pair of statements (X, Y) means "If X is true, then Y must be true" (written as X ⇒ Y), and both statements must be logically consistent with the main statement.

Case 1: Analyzing the pair SP (S implies P)
Statement S is: "Pradeep is not a Producer."
If Pradeep is not a Producer, then to satisfy the main statement ("either a Director or a Producer"), he must be a Director.
Being a Director is Statement P.
Therefore, S implies P (S ⇒ P). This pair is logically consistent with the main statement.

Case 2: Analyzing the pair RQ (R implies Q)
Statement R is: "Pradeep is not a Director."
If Pradeep is not a Director, then to satisfy the main statement ("either a Director or a Producer"), he must be a Producer.
Being a Producer is Statement Q.
Therefore, R implies Q (R ⇒ Q). This pair is also logically consistent with the main statement.

Since both pairs SP and RQ are logically consistent and represent valid implications based on the main statement, the correct option is indeed Both SP and RQ.