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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Consider the statement below.
A person who is radical $(R)$ is electable $(E)$ if he or she is conservative $(C)$, but otherwise is not electable.
Few probable logical assertions of the above sentence are given below.
(A) $(R\land E)\Leftrightarrow C$
(B) $R\Rightarrow(E\Leftrightarrow C)$
(C) $R\Rightarrow((C\Rightarrow E)\lor \neg E)$
(D) $(\neg R\lor \neg E\lor C)\land(\neg R\lor \neg C\lor E)$
Which of the above logical assertions are true?
Choose the correct answer from the options given below:
A person who is radical $(R)$ is electable $(E)$ if he or she is conservative $(C)$, but otherwise is not electable.
Few probable logical assertions of the above sentence are given below.
(A) $(R\land E)\Leftrightarrow C$
(B) $R\Rightarrow(E\Leftrightarrow C)$
(C) $R\Rightarrow((C\Rightarrow E)\lor \neg E)$
(D) $(\neg R\lor \neg E\lor C)\land(\neg R\lor \neg C\lor E)$
Which of the above logical assertions are true?
Choose the correct answer from the options given below:
Solution
Given statement says that a radical person is electable if he or she is conservative, otherwise not electable.This means, for a radical person, electability depends exactly on conservativeness.
So, the correct logical form is:
$R\Rightarrow(E\Leftrightarrow C)$
Therefore, statement (B) is true.
Now,
$E\Leftrightarrow C$
can be written as:
$(E\Rightarrow C)\land(C\Rightarrow E)$
So,
$R\Rightarrow[(E\Rightarrow C)\land(C\Rightarrow E)]$
Now convert implications:
$E\Rightarrow C\equiv \neg E\lor C$
$C\Rightarrow E\equiv \neg C\lor E$
Therefore,
$R\Rightarrow[(\neg E\lor C)\land(\neg C\lor E)]$
This is equivalent to:
$(\neg R\lor \neg E\lor C)\land(\neg R\lor \neg C\lor E)$
So, statement (D) is also true.
Statement (A) is not correct because it says that a person is conservative if and only if the person is radical and electable, which is not the meaning of the given sentence.
Statement (C) is not the exact logical assertion of the given sentence.
Therefore, correct statements are (B) and (D).
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