Question
Download Solution PDFConsider the statement below.
A person who is radical (R) is electable (E) if he/she is conservative (C), but otherwise is not electable.
Few probable logical assertions of the above sentence are given below.
(A) \(\left( {R \wedge E} \right) \Longleftrightarrow C\)
(B) \(R\; \Rightarrow \left( {E \Leftrightarrow C} \right)\)
(C) \(R \Rightarrow \left( {\left( {C \Rightarrow E} \right)V\;\neg \;E} \right)\)
(D) \(\left( {\neg \;R \vee \neg \;E \vee C} \right) \wedge \left( {\neg \;R \vee \neg \;C \vee E} \right)\;\;\)
Which of the above logical assertions are true?
Choose the correct answer from the options given below:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is option 4
Explanation:
1) (R ∧ E) ⟺ C says that all (and only) conservatives are radical and electable. So, this assertion is not true.
2) R ⇒ (E ⇔ C) says that same as the given assertion. This is a correct assertion.
3) R ⇒ ((C ⇒ E) V ¬E) = ¬R∨(¬C∨E∨ ¬E) which is true for all interpretations. This is not a correct assertion.
4) ( ¬ R V ¬ E V C) ∧ (¬ R V ¬ C V E) = (¬ RV( E⇒ C)) ∧ (¬ R V (C ⇒ E)) = R ⇒ (E ⇔ C) which is equivalent to assertion B. This is also true.
Last updated on Jun 19, 2025
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