The Venn diagram for "truth is dependent upon the mind" (by itself) is identical to your diagram, except that the portion of the circle for "World" that is outside the circle for "Mind" is omitted. Hence the conjunction does not set up a contradiction; both statements can indeed be true. If we say instead (as you did above) that "truth is exclusively dependent upon minds," and then add the premiss (as suggested by ↪Terrapin Station) that "minds are part of the world," we get his diagram (Gs=World, Fs=Mind, phi=Truth). In this case, "truth is dependent upon the world" is necessarily true; more precisely, "truth is exclusively dependent upon part of the world." The only way I can see to make the two statements genuinely contradictory is to say that "truth is exclusively dependent upon minds" and "minds are not part of the world." — aletheist
Again 'Truth is exclusively dependent upon minds"
Is not logically equivalent to the statement
"Truth is dependent upon mind and upon the world"
One has a logical connective and the other does not.
So if in the diagram it were that
φ = "truth is exclusively mind dependent"
this leads to a contradiction because
φ is itself dependent upon F, which in Turn is dependent upon G.
That is to say if there is no F and/or no G, then there is no φ by definition.
So the diagram above cannot hope to illustrate that φ="truth is exclusively mind dependent" without also being in contradiction because as you should notice that φ is dependent upon F, which is dependent upon G.
Let us say you hope to redeem the diagram and state that φ=any and all truth
Then it is not true that "Some G's are not F's" without arriving at a contradiction.
The statement "Some G's are not F's" cannot be true(found only in set F). If Some G's are not F's this is only true if it also true that not all φ are F dependent.
If all φ are F dependent then it is not true that some G's are not F's.
Or in other words some G's (those which are not F's) have the property φ.
Hence the diagram is wrong/contradictory with the labels you have applied to the variables used in the diagram.
There is also no contradiction between "this product is exclusively for women" and "this product is for people." This becomes clearer if we change the second premiss to "this product is for some people." There would only be a contradiction if the second premiss instead was (as you rewrote it above) "this product is for all people." — aletheist
The only way to avoid contradiction is to say
"This product is exclusively for women and the product is for SOME people"
Using the term people denotes the set containing both men and women which leads to contradiction.