Answer "true" or "false" to the following statements:
1. In the use of Venn diagrams to test the validity of syllogisms, marks are sometimes entered in the diagram for the conclusion.
2. When an X is placed on the arc of a circle, it means that the X could be in either (or both) of the two areas that the arc separates.
3. If an X lies on the arc of a circle, the argument cannot be valid.
4. When representing a universal statement in a Venn diagram, one always shades two of the seven areas in the diagram (unless one of these areas is already shaded).
5. If a completed diagram contains two X's, the argument cannot be valid.
6. If the conclusion asserts that a certain area is shaded, and inspection of the diagram reveals that only half that area is shaded, the argument is valid.
7. If the conclusion asserts that a certain area contains an X and inspection of the diagram reveals that only half an X appears in that area, the argument is valid.
8. If the conclusion is in the form "All S are P," and inspection of the diagram reveals that the part of the S circle that is outside the P circle is shaded, then the argument is valid.
9. If, in a completed diagram, three areas of a single circle are shaded, and placing a circled X in the one remaining area would make the conclusion true, then the argument is valid from the Aristotelian standpoint but not from the Boolean standpoint.
10. If, in a completed diagram, three areas of a single circle are shaded, but the argument is not valid from the Boolean standpoint, then it must be valid from the Aristotelian standpoint.