# If A happens, then B happens...

• Nov 23rd 2008, 03:38 PM
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?"
• Nov 23rd 2008, 03:42 PM
chiph588@
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
• Nov 23rd 2008, 03:55 PM
masters
Quote:

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"