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A logical binary relation $\odot$, is defined as follows: 

$$\begin{array}{|l|l|l|} \hline \textbf{A} & \textbf{B}& \textbf{A} \odot \textbf{B}\\\hline \text{True} & \text{True}& \text{True}\\\hline \text{True} & \text{False}& \text{True}\\\hline \text{False} & \text{True}& \text{False}\\\hline \text{False} & \text{False}& \text{True}\\\hline   \end{array}$$

Let $\sim$ be the unary negation (NOT) operator, with higher precedence then $\odot$.

Which one of the following is equivalent to $A\wedge B$ ?

  1. $(\sim A\odot B)$
  2. $\sim(A \odot \sim B)$
  3. $\sim(\sim A\odot\sim B)$
  4. $\sim(\sim A\odot B)$
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8 Answers

3 votes
3 votes

Make the K-Map , then write the expression and check the options.

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0 votes
A B ~A ~B (~A op B) ~(A op ~B) ~(~A op ~B) ~(~A op B)   A ⋀ B
T T F F F F F T T
T F F T T F T F F
F T T F T F F F F
F F T T T T F F F

op is the binary logical realtion mentioned in the question.

So second last column i.e. option D matches AND operation of A,B.

Answer:

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