English to symbolic form (transcription)

In summary, you will need to transcribe the given rules into symbolic form, create a truth table, and test different switch combinations until you find one that satisfies all of the rules in order to attach the Mark 13 printer to the Lemon III computer.
  • #1
njama
216
1

Homework Statement



Hello!

I got another problem:

In order to attach the Mark 13 printer to the Lemon III computer, you must set eight "dip switches" in the computer according to the following rules. The switches are labeled a through h and are set to be either ON or OFF.

(1) Neither a nor c is set the same as d.

(2) b and g are different if and only if e and g are in the same positions.

(3) g is OFF if d is OFF, but g is ON if b is OFF.

(4) d is ON, unless e is the same as f.

(5) b is not the same as a if either b or e is OFF.

(6) g is OFF only if e is not the same as h.

(7) b,f, and g are not all the same.

How should the switches be set?

Homework Equations





The Attempt at a Solution



I guess I need to transcribe them in symbolic form. Then create truth table and find values where the truth table is ON (i.e true) so that the Lemon III computer will work. (Maybe I will simplify all of the (1)-(7) before proceeding with truth tables).

The problem is that I do not know how to transcribe them.

First let me denote a,b,c, ..., f as a,b,c,...,f is ON.

Now:

(1) ~(a v c) <-> d

(2) ~( b <-> d) -> (e <-> g)

(3) (~d -> ~g) ^ (~b -> g)

(4) (e <-> f) -> d

(5) (~b v e) -> ~(b <-> a)

(6) ~g -> ~(e <-> h)

(7) ~(b<->f<->h)


Are this transcriptions correct?
 
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  • #2




Yes, your transcriptions seem to be correct based on the given rules. From here, you can create a truth table and systematically test different combinations of switch positions to see which ones satisfy all of the rules. Once you find a combination that satisfies all of the rules, you can set the switches accordingly for the Lemon III computer to work with the Mark 13 printer.
 
  • #3


Yes, your transcriptions appear to be correct. However, it may be helpful to use symbols that are more commonly used in logic, such as ∧ for "and", ∨ for "or", and ¬ for "not". Additionally, it may be clearer to use the symbols = for "is the same as" and ≠ for "is not the same as". So, the transcriptions could be written as:

(1) ¬(a ∨ c) ↔ d

(2) ¬(b ↔ d) → (e ↔ g)

(3) (¬d → ¬g) ∧ (¬b → g)

(4) (e ↔ f) → d

(5) (¬b ∨ e) → ¬(b ↔ a)

(6) ¬g → ¬(e ↔ h)

(7) ¬(b ↔ f ↔ h)

From here, you could proceed with creating a truth table and finding the values that make the statements true. Good luck with your problem!
 

What is English to symbolic form transcription?

English to symbolic form transcription is the process of converting English language into a symbolic or mathematical form. This is often used in fields such as logic, mathematics, and computer science.

Why is English to symbolic form transcription important?

English to symbolic form transcription allows for complex ideas and concepts to be expressed in a concise and precise manner. This makes it easier for scientists and researchers to discuss and analyze complex theories and formulas.

What are some common symbols used in English to symbolic form transcription?

Some common symbols used in English to symbolic form transcription include logical operators such as AND (&), OR (|), and NOT (~), as well as mathematical symbols such as +, -, *, /, and =.

What are some challenges in English to symbolic form transcription?

One major challenge in English to symbolic form transcription is the ambiguity of the English language. The same sentence can often be interpreted in multiple ways, making it difficult to accurately transcribe into symbolic form. Another challenge is ensuring that the symbolic form accurately represents the intended meaning of the English sentence.

Are there any tools or software available for English to symbolic form transcription?

Yes, there are various software programs and tools available that can assist with English to symbolic form transcription. These include logic calculators, programming languages, and natural language processing software. However, it is important to carefully review and check the accuracy of the transcription produced by these tools.

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