CSS Prepare

mpt · CSS study notes

Syllogism

Core Rules

  • Two statements (premises) + a conclusion to evaluate as Valid (follows) or Invalid (doesn't follow)
  • Common forms: "All A are B" / "Some A are B" / "No A are B"
  • "All A are B" does NOT mean "All B are A" — the relationship is one-directional
  • "Some A are B" does NOT mean "Some A are NOT B" — "some" just means "at least one," it says nothing about the rest
  • Chain logic only works when the middle term connects properly: "All A are B" + "All B are C" → "All A are C" is valid

Venn Diagram Approach

  • "All A are B" → draw circle A completely inside circle B
  • "No A are B" → draw circles A and B completely separate
  • "Some A are B" → draw circles A and B partially overlapping
  • To check a conclusion, see if it's true in every possible valid diagram for the given statements — if you can draw even one valid diagram where the conclusion fails, it's invalid

Worked Examples

  1. "All cats are animals. All animals need food. Therefore, all cats need food." → Valid (proper chain)
  2. "Some students are athletes. Some athletes are tall. Therefore, some students are tall." → Invalid (the "some" overlaps aren't guaranteed to be the same group)
  3. "All doctors are educated. Some educated people are rich. Therefore some doctors are rich." → Invalid (no direct link established between doctors and the rich subset)
  4. "No reptiles are mammals. All snakes are reptiles. Therefore no snakes are mammals." → Valid
  5. "All pens are tools. Some tools are expensive. Therefore some pens are expensive." → Invalid (same overlap trap as #2)

Drill

  1. "All roses are flowers. Some flowers fade quickly. Therefore some roses fade quickly." — Invalid
  2. "No fish are mammals. All whales are mammals. Therefore no whales are fish." — Valid
  3. "All engineers are graduates. All graduates are literate. Therefore all engineers are literate." — Valid
  4. "Some teachers are writers. All writers are readers. Therefore some teachers are readers." — Valid (the specific "some teachers who are writers" are guaranteed readers since ALL writers are readers)
  5. "All squares are rectangles. No rectangles are triangles. Therefore no squares are triangles." — Valid

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