🧩 Set Logic Quiz: All, Some, and None

🧩 Analytical Reasoning · Quiz 006

Words such as all, some, and none carry exact logical force. Read them as claims about membership, and avoid strengthening a statement beyond what the premises guarantee.

Learning goalInterpret all, some, and none precisely and reason about subsets, overlap, union, and exclusion.

  • 5 questions
  • Foundation
  • Explanations after finishing
Answered 0/5
FoundationIn formal logic, what does the statement "Some A are B" assert?
Need a small nudge?

Some establishes existence but does not specify the full count.

UnderstandingAll squares are rectangles. Shape X is a square. What must be true?
Need a small nudge?

Place the set of squares inside the set of rectangles.

ApplicationSome tools in a drawer are broken. All broken tools are marked for disposal. Which conclusion is guaranteed?
Need a small nudge?

Follow at least one guaranteed broken tool through the rule about all broken tools.

InterpretationIn a group, 18 people study French, 12 study Spanish, and 5 study both. How many study at least one of the two languages?
Need a small nudge?

Adding 18 and 12 counts the overlap twice.

ConnectionAll R are S. No S are T. At least one R exists. Which conclusion must be true?
Need a small nudge?

Place R inside S, then keep S separate from T.

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