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If I have two statement, say A and B. From which, I formed two formulae:

F1: (not A) and (not B)

F2: (not A) or (not B)

Do F1 and F2 entail each other? In other words, are they equivalent?

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    $\begingroup$ "Do F1 and F2 entail each other?" by this do you mean that whether (a |= b) and (b |= a) ? $\endgroup$ – kiner_shah Jan 28 '17 at 13:37
  • $\begingroup$ @kiner_shah Yes. I meant that. F1 |= F2 and vice-versa. $\endgroup$ – Coder Jan 28 '17 at 20:28
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    $\begingroup$ That means you want to prove that whether the two statements are equivalent $\endgroup$ – kiner_shah Jan 29 '17 at 6:11
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After studying and getting answers from experts, I could find out the answer to this question and posting as an answer to my own question.

F1 will entail (|=) F2; if and only if F2 must be true if we assume F1 to be true.

Similarly, F2 will entail (|=) F1; if and only if F1 must be true if we assume F2 to be true.

Logically, by taking any value for A or B, from the domain {TRUE, FALSE}, one could verify that F1 entails F2. Because, F2 is true; whenever F1 is true (e.g. when both A and B are FALSE).

However, F2 does not entail F1. As, in two cases, F2 is true (e.g. A= FALSE and B=TRUE, or vice-versa), but F1 is not true.

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