How to show this equivalence in first order language ?

Thread starter Maths Lover
Start date Oct 29, 2013
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Equivalence First order Language

In summary, equivalence in first order language can be represented using the biconditional connective "↔" or the word "iff". It is important to use parentheses and consider the placement of quantifiers when showing equivalence. To prove equivalence, one must show that the truth value of one statement is dependent on the truth value of the other statement, using logical equivalences and laws of inference.

Oct 29, 2013

Maths Lover

Here is the question in attachment , I make it as the site don't support LaTeX I think!

https://www.physicsforums.com/attachment.php?attachmentid=63439&stc=1&d=1383093152

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Oct 30, 2013

UltrafastPED

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Yes, LaTex is supported; see https://www.physicsforums.com/showthread.php?t=617567

1. How do I represent equivalence in first order language?

Equivalence in first order language can be represented using the biconditional connective "↔". This symbol is placed between two statements to show that they are logically equivalent.

2. Can I use symbols other than "↔" to show equivalence?

Yes, there are other symbols that can be used to show equivalence in first order language. For example, the word "iff" (if and only if) can also be used as a connective for equivalence.

3. Do I need to use parentheses when showing equivalence in first order language?

Yes, it is important to use parentheses when representing equivalence in first order language. This ensures that the intended meaning is clear and avoids any confusion or ambiguity.

4. Can I use quantifiers when showing equivalence in first order language?

Yes, quantifiers can be used in statements that involve equivalence in first order language. However, it is important to note that the placement of quantifiers can affect the overall meaning of the statement.

5. How do I prove that two statements are equivalent in first order language?

In order to prove equivalence in first order language, you must show that the truth value of one statement is dependent on the truth value of the other statement. This can be done by using logical equivalences and laws of inference.