What are the duals of the following statements?

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  1. Two distinct points are on one and only one line.
  2. There are at least three distinct points that do not lie on the same line.
  3. Points are collinear if they all lie on the same line.
  4. (Desargue's Theorem) If two triangles are so situated that the three lines through the pairs of corresponding vertices are concurrent, then the three intersection points of the pairs of their corresponding sides are collinear.

Help! I'm stuck in a discrete math class and haven't taken the introductory abstract course.

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  1. Two distinct lines intersect at one and only one point.
  2. There are at least three distinct lines that do not intersect at the same point.
  3. Lines are concurrent if they all intersect at the same point.
  4. the dual is the converse, Desargues' thm (if and only if version) is self-dual

another qn which asks for the dual of statements: Dualize this Projective Geometry Statement