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7. If we sell the boat (b), then we will not go to the river (~r). If we don't go to the river, then we will go to camping (c). If we do not buy a tent (~t), then we will not go to camping. Therefore, if we sell the boat then we will buy a tent. 8. If it is an ammonite (a), then it is from cretaceous period (c). If it is not from Mesozoic era (~m), then it is not from the cretaceous period. It is from Mesozoic era, then it is at least 65 million years old (s). Therefore, if it is an ammonite, then it is at least 65 million years old. 9. If the computer is not operating (~0), then I will not be able to finish my report (~f). If the office is closed (c), then the computer is not operating. Therefore, if I am able to finish my report, then the office is open.

7. If we sell the boat (b), then we will not go to the river (~r). If we don't go to the river, then we will go to camping (c). If we do not buy a tent (~t), then we will not go to camping. Therefore, if we sell the boat then we will buy a tent. 8. If it is an ammonite (a), then it is from cretaceous period (c). If it is not from Mesozoic era (~m), then it is not from the cretaceous period. It is from Mesozoic era, then it is at least 65 million years old (s). Therefore, if it is an ammonite, then it is at least 65 million years old. 9. If the computer is not operating (~0), then I will not be able to finish my report (~f). If the office is closed (c), then the computer is not operating. Therefore, if I am able to finish my report, then the office is open.

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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In exercises 7-10, use a sequence of valid arguments to show that each argument is valid. (Make the solution TYPEWRITTEN) 7. If we sell the boat (b), then we will not go to the river (~r). If we don't go to the river, then we will go to camping (c). If we do not buy a tent (~t), then we will not go to camping. Therefore, if we sell the boat then we will buy a tent. 8. If it is an ammonite (a), then it is from cretaceous period (c). If it is not from Mesozoic era (~m), then it is not from the cretaceous period. It is from Mesozoic era, then it is at least 65 million years old (s). Therefore, if it is an ammonite, then it is at least 65 million years old. 9. If the computer is not operating (~0), then I will not be able to finish my report (~f). If the office is closed (c), then the computer is not operating. Therefore, if I am able to finish my report, then the office is open. 10. If he reads the manuscript (r), he will like it. (1) If he likes it, he will publish it (p). If he publishes it, then you will get royalties (m). You did not get royalties. Therefore, he did not read the manuscript. NOTE: please refer to the given lesson for reference
Example 4.5 In each argument, use all premises to determine the valid conclusion. 1. We will not go to japan (j) or we will go to Hong Kong (h). If we visit my uncle (u). then we will go to Singapore (s). If we go to Hong Kong then we will not go to Singapore. Solution: Write the argument in symbolic form. ~jvh UIS h→-s Premise 1 Premise 2 Premise 3 The first premise can be written as j→→h. The contrapositive of the second premise is ~s →→~u. Therefore the argument can be written as j-h Interchanging the second and third premises yields 11 h→-s j-h h--s 11U By transitive reasoning the valid conclusion will be ju. Thus the valid conclusion for the argument is "If we go to Japan, then we will not visit my uncle."
Transcribed Image Text:Example 4.5 In each argument, use all premises to determine the valid conclusion. 1. We will not go to japan (j) or we will go to Hong Kong (h). If we visit my uncle (u). then we will go to Singapore (s). If we go to Hong Kong then we will not go to Singapore. Solution: Write the argument in symbolic form. ~jvh UIS h→-s Premise 1 Premise 2 Premise 3 The first premise can be written as j→→h. The contrapositive of the second premise is ~s →→~u. Therefore the argument can be written as j-h Interchanging the second and third premises yields 11 h→-s j-h h--s 11U By transitive reasoning the valid conclusion will be ju. Thus the valid conclusion for the argument is "If we go to Japan, then we will not visit my uncle."
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