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​​​​​​​Consider a vocabulary with only four propositions A, B, C and D. How many models are there for the following sentence?

$\neg A \vee \neg B \vee \neg C \vee \neg D$

  1. $7$
  2. $8$
  3. $15$
  4. $16$
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3 Answers

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$\sim A\vee \sim B\vee \sim C \vee \sim D$ is nothing but OR of $\sim A$, $\sim B$,$\sim C$ and $\sim D$

The truth table of the following model is shown below

$\sim A$ $\sim B$ $\sim C$ $\sim D$  Output
0 0 0 0 0
0 0 0 1 1
0 0 1 0 1
0 0 1 1 1
0 1 0 0 1
0 1 0 1 1
0 1 1 0 1
0 1 1 1 1
1 0 0 0 1
1 0 0 1 1
1 0 1 0 1
1 0 1 1 1
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1

Since there are 15 $1's$ in the truth table

$\therefore$ option C. should be the correct answer

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There are four variables A,B,C,D. Therefore 2^4= 16 total 16 element so 0 to 15  15 is the right answer
Option c is the correct answer

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