Do truth tables accurately prove equality and inequality between sets?

[lordy12]

Are truth tables acceptable forms of proving the
equality and inequality between sets.
For example, A U (B^C) = (AUB) ^(AUC)

A B C AU(B^C) (AUB)^(AUC)
F F F F F
F F T F F
F T F F F
F T T T T
T F F T T
T F T T T
T T F T T

 

[HallsofIvy]

Strictly speaking, sets do not have truth values. I presume that what you have labled "A" is actually the statement "x is contained in A", etc.

Given that, how have you arrived at the truth values for the statements
"x is contained in AU(B^C)" and "x is contained in (AUB)^(AUC)"?

 

[matt grime]

Truth tables are never acceptable (for either moral or technical reasons) proofs of anything other than statements about truth tables.

The fact that A implies B is true if either A is false or A is true and B is true is neither here nor there: it doesn't ever show that in some particular situation A can be used to deduce B. Do you understand the distinction? (Probably not or you wouldn't have asked the question.)

 

[Crosson]

Do you understand the distinction?

The confusion arises from the mathematicians use of $$\Rightarrow$$.

When a mathematician says $$A \Rightarrow B$$ he means that there is a valid argument:

1) A
2) Theorems discussed in context prior to A
3) All knowledge prerequisite to this discussion
.
.
.
Therefore, B.

In other words, $$\Rightarrow$$ has nothing to do with deduction, and logic reflects this, but the usage of $$\Rightarrow$$ by mathematicians does not! Instead we should circumlocute "A, therefore B", less students remained confused forever.