Syllogisms
Deciding which conclusions follow from All, Some and No statements by drawing every possible Venn diagram — including possibility conclusions and either-or conclusions.
What you will be able to do
- Draw All, Some and No statements as circle diagrams.
- Test a conclusion by trying to draw the statements so it fails.
- Judge a possibility conclusion against the set of valid diagrams.
- Recognise when two conclusions form an either-or pair.
What is inside this lesson
- 1What 'follows' means
- 2Draw the statements as circles
- 3How 'Some' and 'All' behave
- 4Testing a conclusion
- 5Possibility and either-or conclusions
- 6Worked example
- 7Common mistakes
- 8Quick revision
- 9Practice
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What 'follows' means
A syllogism gives two or more statements built from All, Some and No, then a few conclusions. You must say which conclusions follow.
A conclusion follows only if it is true in every arrangement the statements allow. If you can draw even one valid picture where the conclusion fails, it does not follow. Treat the statements as certainly true, however odd they sound, and never bring in outside knowledge about the real things named.
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