Let A be an apple growing

Let B a fruit growing

If A then B:

if an apple has grown then a fruit has grown

but if an apple hasn't grown then a fruit still could've grown i.e. like an orange

therefore invalid

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- Nov 23rd 2008, 03:38 PM #1
## If A happens, then B happens...

Please help me:

In the following case, I can't decide if it's valid or invalid because I don't know if B HAS to happen if A happens. Can someone clarify?

"If A happens, then B happens.

A does not happen.

Therefore, B does not happen.

VALID/INVALID, WHY?"

- Nov 23rd 2008, 03:42 PM #2

- Nov 23rd 2008, 03:55 PM #3

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If a statement is true, then its contrapositive is true. A statement and its contrapositive are logically equivalent.

"If A, then B is TRUE", then the contrapositive would be "If not B is TRUE, then not A is TRUE"

Using your statements:

(1) If A, then B

(2) Not A

(3) Therefore, not B

Your second statement is not the contrapositive of the first statement. It is the inverse of the first statement. Therefore, not logically equivalent; therefore INVALID conclusion.

A valid argument would have been:

(1) If A, then B

(2) Not B

(3) Therefore, not A

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