Question

Consider the statement that min(a, min(b, c)) = min(min(a, b), c) whenever a, b, and c...

Consider the statement that min(a, min(b, c)) = min(min(a, b), c) whenever a, b, and c are real numbers.

Identify the set of cases that are required to prove the given statement using proof by cases.

Multiple Choice. Choose correct one.

  • a ≤ b ≤ c, a ≤ c ≤ b, b ≤ a ≤ c, b ≤ c ≤ a, c ≤ a ≤ b, c ≤ b ≤ a

  • a>b>c, a>c>b, b>a>c, b>c>a, c>a>b, c>b>a.a>b>c, a>c>b, b>a>c, b>c>a, c>a>b, c>b>a.

  • a≥b≥c, a≥c≥b, b≥a≥c, b≥c≥a, c≥a≥b, c≥b≥a.a≥b≥c, a≥c≥b, b≥a≥c, b≥c≥a, c≥a≥b, c≥b≥a.

  • a<b<c, a<c<b, b<a<c, b<c<a, c<a<b, c<b<a.

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