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The astronomer Johannes Kepler studied massive amounts of data on the positions of the planets.
1. The astronomer Johannes Kepler studied massive amounts of data on the positions of the planets. On the basis of this data, he concluded that the planets move around the sun in elliptical orbits. Was Kepler's conclusion a result of deductive or inductive reasoning? Explain your answer by contrasting Kepler's reasoning with the other type of reasoning and give one example of this other type of reasoning.
2. Explain whether the following statement is a valid definition: "A square is a figure with four right angles." Use the converse, biconditional, and at least one Euler diagram to support your answer.
3. Start with the following statement:
Every square is a rhombus.
a.) State the conditional and three other forms of the statement.
b.) If you know that a statement is true, what do you know about the truth of its converse, inverse, and contrapositive? Use at least one truth table and at least one property to support your reasoning.
