# Have I drawn this Venn diagram correctly?

Does this look correct?

https://i.sstatic.net/A4jlS.png

I'm trying to find out whether this syllogism is valid (I'm guessing it's not valid)

Many thanks

• What do the shaded areas mean?
– 5xum
Commented Jun 3, 2015 at 8:49
• Basically by shading out what I have, what's left is all cacti are plants (the intersection part) - by shading this out, this region does not exist anymore Commented Jun 3, 2015 at 8:50
• And what does the red cross mean? I don't really get how drawing 3 circles proves or disproves your syllogism...
– 5xum
Commented Jun 3, 2015 at 8:53
• the red cross means some plants are green- but because there are two regions to pick it goes on the bit where C intersects G it's using a venn diagram method.. very common Commented Jun 3, 2015 at 8:55
• OK, and how can you conclude anything about your syllogism from this?
– 5xum
Commented Jun 3, 2015 at 8:56

The following argument is invalid:

(P1): All Cacti are Plants. (P2): Some Plants are Green. Conclusion: Some Cacti are not Green.

It's just that the non-Green plants needn't have any Cacti among them. The Venn diagram below illustrates that. Note that the diagram satisfies both (P1) and (P2), as required.

No, you're not satisfying the first condition because the way you drew it says that not all C are P.

• No it doesnt? i shaded out the region that would say 'not all c are p' lol (this is from what I've learnt anyway..) Commented Jun 3, 2015 at 8:47
• It is not clear from the diagram that you have shaded out what is not relevant. Commented Jun 3, 2015 at 8:55
• @prime4567 everywhere I've read seems to be using this rule as standard practice Commented Jun 3, 2015 at 8:55

Well, if I got it right:

You draw three circles that show all possibilities of things being cacti, plants and green.

You shade areas that you know are empty (from premises) and you mark with red x an area known to be not empty (since some plants are green).

Now, all unshaded and separated areas may have something in them or they may be empty. We just do not know.

Conclusion declares that some cacti are not green. This area in our Venn diagram is unshaded. It may have something in it or it may be empty. Therefore we can not make such conclusion.

If we accept silent premise that there are some cacti (danger!) then we have also look if cacti$\times$not green is only area where cacti may be. If so, our conclusion should be true (given silent premise). But from our Venn diagram we see that there is other area, where cacti can be, namely cacti$\times$green. So we can not make that conclusion and syllogism is false.