# Truth table for this claim?

A simple question for all you logicians out there, I'm sure:

"An adaptive household has a diverse livehood portfolio and is healthy, but is not always natural resource reliant."

Is there a way to express this? p,q,r=livelihood, health, and natural resource reliance, respectively. I guess r would be expressed as the subjunctive mood, but I don't know if that applies in sentential logic.

Thanks!

• p AND q AND (NOT r) would be one way of doing things, provided p q r stood for the appropriate propositions Commented Aug 2, 2013 at 15:00

What may be tripping you up is that the truth of "household is natural resource reliant" has no impact at all on the truth of "household is adaptive".

...so the formula for what you've said is:
"is adaptive" = "has diverse livehood portfolio" AND "is healthy"

The truth table would be (with no "household is adaptive" listed, because it is unnecessary):

• "has diverse livehood portfolio" ; "is healthy" : "is adaptive"
• 0 ; 0 : 0
• 0 ; 1 : 0
• 1 ; 0 : 0
• 1 ; 1 : 1

If you really want to include "is natural resource reliant", you would end up with:

• "has diverse livehood portfolio" ; "is healthy" ; "is natural resource reliant" : "is adaptive"
• 0 ; 0 ; 0 : 0
• 0 ; 0 ; 1 : 0
• 0 ; 1 ; 0 : 0
• 0 ; 1 ; 1 : 0
• 1 ; 0 ; 0 : 0
• 1 ; 0 ; 1 : 0
• 1 ; 1 ; 0 : 1
• 1 ; 1 ; 1 : 1

...where, again, you can see that "is natural resource reliant" has no impact.

• Is that the same as the syntax David H. mentioned? Commented Aug 3, 2013 at 2:09
• @LannyYassier No. p AND q AND (NOT r) would match the statement "An adaptive household has a diverse livehood portfolio and is healthy, but is not natural resource reliant." p AND q is what matches the statement you gave.
– A.M.
Commented Aug 3, 2013 at 2:22
• @LannyYassier Of course there are two ways to read "not always x". I read it as "not always [natural resource reliant]", whereas he appears to have read it as "not [always natural resource reliant]", in which case his formula would be correct.
– A.M.
Commented Aug 3, 2013 at 2:26