UGC NET CSE | October 2020 | Part 2 | Question: 61

Question

Consider the statement below.

A person who is radical $(R)$ is electable $(E)$ if he/she is conservative $(C)$, but otherwise not electable.

Few probable logical assertions of the above sentence are given below.

1. $(R \wedge E) \Leftrightarrow C$
2. $R \rightarrow (E \leftrightarrow C)$
3. $R \Rightarrow ((C \Rightarrow E) \vee \neg E)$
4. $(\neg R \vee \neg E \vee C) \wedge (\neg R \vee \neg C \vee E)$

Which of the above logical assertions are true?

Choose the correct answer from the options given below:

• A. $(ii)$ only
• B. $(iii)$ only
• C. $(i)$ and $(iii)$ only
• D. $(ii)$ and $(iv)$ only

Answer 1

A person who is radical (R) is electable (E) if he/she is conservative (C), but otherwise not electable.

this simply means {R --->(C<---->E)} option B 

it can be expanded as (R-->(C-->E ∧ E-->C))

(¬R∨(¬C∨E)∧(¬E∨C))

=(¬R∨¬E∨C)∧(¬R∨¬C∨E)  option D 

Hence ans is option D)   (B) and (D)only