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Drawing Affirmative Conclusion

The conclusion of a standard form categorical syllogism is affirmative, but at least one of the premises is negative.

Examples
  1. All mice are animals, and some animals are not dangerous, therefore some mice are dangerous.
  2. No honest people steal, and all honest people pay taxes, so some people who steal pay taxes.
Critique
Assume that the premises are true. Find an example which allows the premises to be true but which clearly contradicts the conclusion.