Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Common Proof Tools This list serves as a reminder of proof justifications you may use throughout the homework. We are providing the following here as hints for your homework, however, this list will not be provided on an exam 1. x is even if and only if x is even 2. x is odd if and only if x is odd 3. Multiplication is closed under integers 4. Addition is closed under integers 5. The definition of a biconditional states that p ↔ q is equivalent to p→ q^q→p 6. The list is not all inclusive and does not include other definitions learned in class and algebraic properties learned elsewhere
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Transcribed Image Text:Common Proof Tools This list serves as a reminder of proof justifications you may use throughout the homework. We are providing the following here as hints for your homework, however, this list will not be provided on an exam 1. x is even if and only if x is even 2. x is odd if and only if x is odd 3. Multiplication is closed under integers 4. Addition is closed under integers 5. The definition of a biconditional states that p ↔ q is equivalent to p→ q^q→p 6. The list is not all inclusive and does not include other definitions learned in class and algebraic properties learned elsewhere
3. Use a direct proof to show that if x +y is even, then x²y - y³ + 2 is even. Clearly state your reasoning for all statements and use a two-column proof for the body whenever possible. You should include an intro, body (in two column format), and a conclusion. (Hint: It might be beneficial to factor r²y - y³ in your scratch work)
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Transcribed Image Text:3. Use a direct proof to show that if x +y is even, then x²y - y³ + 2 is even. Clearly state your reasoning for all statements and use a two-column proof for the body whenever possible. You should include an intro, body (in two column format), and a conclusion. (Hint: It might be beneficial to factor r²y - y³ in your scratch work)
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