Discrete Mathematics Puzzle

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Across
  1. 2. A counting principle used to avoid double-counting overlapping elements.
  2. 4. A collection of non-overlapping subsets whose union is the original set.
  3. 5. A structure-preserving mapping showing that two algebraic systems are essentially identical.
  4. 8. The property of an argument being logically sound with no contradictions.
  5. 9. The negated and reversed form of an implication that retains its logical equivalence.
Down
  1. 1. A function that maps distinct inputs to distinct outputs.
  2. 3. Relates to the minimum number of colors required for proper vertex coloring of a graph.
  3. 4. An arrangement of objects in a specific order where sequence matters.
  4. 6. A circuit that visits every edge exactly once in a connected graph.
  5. 7. A logical statement that is true for some truth assignments and false for others.