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Consider the example "For every integer n, if n> 2 then n2> 4." In this case p represents “n> 2" and q represents "n?> 4." Thus if n= 3 then p is true and q is true. (a) Find another value of n that makes p true and q true. (b) Find a value for n that makes p false and q false. (c) Find a value for n that makes p false and q true. (d) Find a value for n that make p true and q false. Explain any problems you have. Why are you having these problems? The third row, corresponding to part (c), frustrates many people-you are not alone. The truth has a special name. It is called "vacuously true."

Consider the example "For every integer n, if n> 2 then n2> 4." In this case p represents “n> 2" and q represents "n?> 4." Thus if n= 3 then p is true and q is true. (a) Find another value of n that makes p true and q true. (b) Find a value for n that makes p false and q false. (c) Find a value for n that makes p false and q true. (d) Find a value for n that make p true and q false. Explain any problems you have. Why are you having these problems? The third row, corresponding to part (c), frustrates many people-you are not alone. The truth has a special name. It is called "vacuously true."

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the example "For every integer n, if n>2 then n2> 4." In this case p represents “n> 2" and q represents “n?> 4." Thus if n= 3 then p is true and q is true. (a) Find another value of n that makes p true and q true. (b) Find a value for n that makes p false and q false. (c) Find a value for n that makes p false and q true. (d) Find a value for n that make p true and q false. Explain any problems you have. Why are you having these problems? The third row, corresponding to part (c), frustrates many people-you are not alone. The truth has a special name. It is called “vacuously true."
Transcribed Image Text:Consider the example "For every integer n, if n>2 then n2> 4." In this case p represents “n> 2" and q represents “n?> 4." Thus if n= 3 then p is true and q is true. (a) Find another value of n that makes p true and q true. (b) Find a value for n that makes p false and q false. (c) Find a value for n that makes p false and q true. (d) Find a value for n that make p true and q false. Explain any problems you have. Why are you having these problems? The third row, corresponding to part (c), frustrates many people-you are not alone. The truth has a special name. It is called “vacuously true."
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