NIELIT Scientist B 2020 November: 84

Question

Given the truth table of a Binary Operation \$ as follows:

$$\begin{array}{|l|l|l|l|} \hline {}   \text{X}  &  \text{Y }&  \text{X\$Y }\\ \hline  \text{1}  &  \text{0 }&  \text{1 }\\ \hline  \text{1}  &  \text{1}&  \text{1 }\\ \hline  \text{0}  &  \text{1 }&  \text{0 }\\ \hline  \text{0}  &  \text{0 }&  \text{1 }\\ \hline  \end{array}$$

Identify the matching Boolean Expression.

• A. $X \$ \neg Y$
• B. $\neg X \$ Y$
• C. $\neg X \$ \neg Y$
• D. none of the options

Comments

Detailed Video Solution: NIELIT Scientist B 2020 November: 84 ViDEO Solution 

Answer 1

Given that,

$$\begin{array}{|c|c|c|} \hline X & Y & X\$ Y \\\hline 1 & 0 & 1 \\\hline 1 & 1 & 1 \\\hline 0 & 1 & 0 \\\hline 0 & 0 & 1 \\\hline \end{array}$$

Here, $X\$ Y\equiv Y \rightarrow X \equiv \neg Y \vee X \equiv X \vee \neg Y$

Now, we can check each options, 

• A. $X \$ \neg Y \equiv \neg Y \rightarrow  X \equiv \neg(\neg Y) \vee X\equiv Y \vee X \equiv X \vee Y$
• B. $\neg X \$ Y \equiv Y \rightarrow \neg X \equiv \neg Y \vee \neg X \equiv \neg X \vee \neg Y$
• C. $\neg X \$ \neg Y \equiv \neg Y \rightarrow \neg X \equiv \neg(\neg Y) \vee \neg X \equiv Y \vee \neg X \equiv \neg X \vee Y$

None of the option matches.

So, the correct answer is $(D).$

Comments

This is just a brilliant question and that is an even more beautiful solution! :) There is a huge scope for making silly mistakes even after knowing all the questions, in an exam environment.

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Really Awesome problem,

So,Here First we need to find out what will be the operator used in X$Y.

Second Step is to derive the options on the basis of the Operator $.

Third step is whatever solution matches with x$y then that will be the solution.So Here Y → X = Y v ~X = ~X v Y. If any option Matched with these two compound propositions.But here None of the options matched.So, Option D is solution