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.

EXPLANATION

Correct Option (3)

The Main Statement "Pradeep becomes either a Director or a Producer" implies an inclusive disjunction. This means Pradeep is a Director, or Pradeep is a Producer, or both. It explicitly excludes the possibility of Pradeep being neither a Director nor a Producer.

Let's analyze the pairs:

Pair SP:
- Statement S: Pradeep is not a Producer.
- Statement P: Pradeep is a Director.
- If Pradeep is not a Producer (Statement S), then for the Main Statement (Pradeep is a Director OR Pradeep is a Producer) to remain true, Pradeep must necessarily be a Director. Therefore, Statement S implies Statement P.
- The combined state of Pradeep being not a Producer and being a Director is consistent with the Main Statement.
Pair RQ:
- Statement R: Pradeep is not a Director.
- Statement Q: Pradeep is a Producer.
- If Pradeep is not a Director (Statement R), then for the Main Statement (Pradeep is a Director OR Pradeep is a Producer) to remain true, Pradeep must necessarily be a Producer. Therefore, Statement R implies Statement Q.
- The combined state of Pradeep being not a Director and being a Producer is consistent with the Main Statement.

Both pairs, SP and RQ, satisfy the conditions that the first statement implies the second, and both statements are logically consistent with the Main Statement.

Incorrect Options:

Option 1 (SP only): This option is incorrect because while the pair SP is valid, the pair RQ is also valid, making this option incomplete.
Option 2 (RQ only): This option is incorrect because while the pair RQ is valid, the pair SP is also valid, making this option incomplete.
Option 4 (Neither SP nor RQ): This option is incorrect because, as demonstrated, both pairs SP and RQ are logically consistent with the Main Statement and satisfy the implication condition.