From the course: Programming Foundations: Discrete Mathematics
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Write a general outline for a proof
From the course: Programming Foundations: Discrete Mathematics
Write a general outline for a proof
- A theorem is a statement that can be proven true or false. A proof consists of a series of steps, each of which follows logically from assumptions or from previously proven statements whose final step should result in a statement of the theorem being proven. Axioms are statements assumed to be true, or previously proven theorems. An example is the definition of even and odd integers. An even integer is any integer that can be represented by two times x, where x is also an integer. 10 is two times five, 200 is two times 100, etcetera. An odd number is represented by any number such that it can be written as two times x plus one. So 11 is two times five, plus one. Proofs fall into two categories, direct and indirect proofs. With an indirect proof, instead of proving that the conclusion is true, you start by assuming that the opposite is true. Then, using deductive reasoning to lead to a contradiction, you can prove the original hypotheses is true. Proof by contradiction is another…
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Write a general outline for a proof4m 48s
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Write subset proofs3m 12s
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Evaluate conditional proofs8m 54s
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Understand biconditional proofs4m 14s
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Prove with mathematical induction10m 40s
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Challenge: Write a proof49s
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Solution: Write a proof4m 23s
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