# Thread: If A happens, then B happens...

1. ## If A happens, then B happens...

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?"

2. 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

3. Originally Posted by pleasehelpme12345

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?"
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"

(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