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GO Classes 2023 | Weekly Quiz 5 | Question: 13

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Consider two formula :

  • $\phi : p\wedge \neg q \rightarrow p\wedge q$
  • $\psi : \neg p$.

Which of the following is/are true?

  1. $\phi$ is a logical consequence of the formula $\psi$
  2. $\psi$ is a logical consequence of the formula $\phi$
  3. $\phi$ is a logically equivalent to the formula $\psi$
  4. Neither $\phi$, nor $\psi$, is a logical consequence of the other.
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1 Answer

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$$\begin{array}{|c|c|c|c|c|c|} \hline p & q &\neg p & p\wedge \neg q & p\wedge q & p\wedge \neg q \rightarrow p \wedge q \\\hline \text{T} & \text{T} & \text{F} & \text{F} & \text{T} & \text{T} \\\hline \text{T} & \text{F} & \text{F} & \text{T} & \text{F} & \text{F} \\\hline \text{F} & \text{T} & \text{T} & \text{F} & \text{F} & \text{T} \\\hline \text{F} & \text{F} & \text{T} & \text{F} & \text{F} & \text{T} \\\hline \end{array}$$
So, $\phi$ is a logical consequence of the formula $\psi$ i.e.,  $\psi \rightarrow \phi$ is true.

Detailed Video Solution:

https://youtu.be/nclBhBmtz2g?t=5147

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