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?

  • 1
    $\begingroup$ "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
  • 1
    $\begingroup$ That means you want to prove that whether the two statements are equivalent $\endgroup$ – kiner_shah Jan 29 '17 at 6:11

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.

| improve this answer | |

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.