Are (A then B) then C and (A and B) then C equivalent?

  • Thread starter Gamecockgirl
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In summary, the conversation revolves around proving the equivalence of the statements "if (A then B) then C" and "if (A and B) then C". The suggested method is to use a truth table with 8 different combinations of A, B, and C. The user also advises to be familiar with the meanings of the statements in order to determine their truth values in each situation.
  • #1
Gamecockgirl
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I need help proving that (A then B) then C and (A and B) then C are equivalent. Can anyone help?
 
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  • #2
This doesn't meet criterai for posting in Philosophy. If this is homework, please post in the appropriate Homework forum
 
  • #3
I am moving this to the "precalculus homework" forum.

Gamecock Girl, I think the simplest way to do this is to use a "truth table". There are 23 different ways A, B, and C can be "True" or "False". The two statements are equivalent if they are both True or both False in each of those.

Writing "T" for True, "F" for False and "ABC" in that order, the 8 ways are:
TTT, TTF, TFT, TFF, FTT, FTF, FFT, FFF. Assuming you know what "if (if A then B) then C" and "if (A and B) then C" mean, you can decide whether they are True of False in each of those 8 situations.
 

What does it mean to prove two things are equivalent?

Proving two things are equivalent means showing that they have equal value, meaning, or function. It involves demonstrating that one can be transformed into the other without altering its properties or characteristics.

Why is it important to prove equivalence?

Proving equivalence is important in fields such as mathematics, science, and engineering because it allows us to make connections between seemingly different concepts and understand their relationships. It also helps us to simplify complex problems and find more efficient solutions.

What are some methods for proving equivalence?

Some common methods for proving equivalence include using logical reasoning, mathematical equations and formulas, and comparing properties and characteristics. Other techniques may involve constructing counterexamples or using proof by contradiction.

Can two things be equivalent but not identical?

Yes, two things can be equivalent but not identical. Equivalence means that they have the same value or function, but they may have different properties or characteristics. For example, two different mathematical equations can be equivalent in terms of their solutions, but they may have different forms.

How can we use the concept of equivalence in everyday life?

The concept of equivalence is applicable in everyday life in various ways. For example, we can use it to convert currencies when traveling, compare prices of similar products, or understand the relationship between different units of measurement. It can also help us make decisions by evaluating the trade-offs between different options that are equivalent in value or function.

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