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Given a set of N different elements. Let's say, elements of this set are numbers from 1 to N. How many subset does this set have?
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Given two sets. Set A contains elements: book, pen, football, building, planet. Set B contains elements: football, golf ball, tennis ball. What set is a result of an operation of intersection between sets A and B?
Given a set: book, pen, football, building, planet. How many elements does this set have? What are they? What subsets, including trivial, does this set have? What elements belong to a subset of "man- made things"?
Prove using the method of mathematical induction that N straight lines on a plain cross in N*(N- 1)/2 points provided there are no parrallel lines among them and no points where more than 2 lines cross each other.
Prove using the method of mathematical induction that the sum of internal angles of convex polygon with N sides is equal to 180*(N- 2) degrees.
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