- #1

- 36

- 0

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

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- Thread starter lordy12
- Start date

- #1

- 36

- 0

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

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 963

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)"?

- #3

matt grime

Science Advisor

Homework Helper

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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.)

- #4

- 1,250

- 2

Do you understand the distinction?

The confusion arises from the mathematicians use of [tex]\Rightarrow[/tex].

When a mathematician says [tex] A \Rightarrow B[/tex] 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, [tex] \Rightarrow [/tex] has nothing to do with deduction, and logic reflects this, but the usage of [tex]\Rightarrow [/tex] by mathematicians does not! Instead we should circumlocute "A, therefore B":yuck:, less students remained confused forever.

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