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4. If I mastered college algebra (c), then I will be prepared for trigonometry (t). I am prepared for trigonometry. Therefore, I mastered college algebra. 5. If it is a blot (b), then it is not a clot (c). If it is a zlot (z), then it is a clot. It is a blot. Therefore, it is not a zlot.

4. If I mastered college algebra (c), then I will be prepared for trigonometry (t). I am prepared for trigonometry. Therefore, I mastered college algebra. 5. If it is a blot (b), then it is not a clot (c). If it is a zlot (z), then it is a clot. It is a blot. Therefore, it is not a zlot.

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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Please answer items 4 and 5 only. Use the attached lesson for reference
LEARNING ACTIVITY 4.2 Use truth table to determine whether each argument is valid or invalid. 1. If you finish your homework (h), then you may attend the reception (r). You did not finish your homework Therefore, you cannot go to the reception. 2. If I cannot buy the house (~b) est I can dream about it (d). I can buy the house or at least I can dream about it erefore, I can buy the house. 3. If the us are from the east (e), then we will not have a big surf (s). We do not have a big Therefore, the winds are from the east. 4. If I mastered college algebra (c), then I will be prepared for trigonometry (t). I am prepared for trigonometry. Therefore, I mastered college algebra. 5. If it is a blot (b), then it is not a clot (c). If it is a zlot (z), then it is a clot. It is a blot. Therefore, it is not a zlot.
Transcribed Image Text:LEARNING ACTIVITY 4.2 Use truth table to determine whether each argument is valid or invalid. 1. If you finish your homework (h), then you may attend the reception (r). You did not finish your homework Therefore, you cannot go to the reception. 2. If I cannot buy the house (~b) est I can dream about it (d). I can buy the house or at least I can dream about it erefore, I can buy the house. 3. If the us are from the east (e), then we will not have a big surf (s). We do not have a big Therefore, the winds are from the east. 4. If I mastered college algebra (c), then I will be prepared for trigonometry (t). I am prepared for trigonometry. Therefore, I mastered college algebra. 5. If it is a blot (b), then it is not a clot (c). If it is a zlot (z), then it is a clot. It is a blot. Therefore, it is not a zlot.
Example 4.2 Use truth table to determine whether the argument is valid or invalid. 1. If it rains, then the game will not be played. It is not raining. Therefore, the game will be played. Solution: Let r represents "it rains" and g represents "the game will be played". The symbolic form of the argument will be: r-g Ag Now let us construct truth table. r Solution: Label each simple statement. T T F F m-s s t -t-~m m T T T Construct truth table. T F Notice on the preceding table that row 4, where both premises are true, produced false conclusion. This is enough to say that the argument is invalid. m: I am going to run the marathon s: I will buy new shoes. t: I will buy a television. The symbolic form of the argument is: F 2. If I am going to run the marathon, then I will buy new shoes. If I buy new shoes, I will not buy a television. Therefore If I buy a television, I will not run the marathon. F F F S T T F F 8 T F T F T T F F t T F T F = First Premise Second Premise Conclusion R T r~g F T T T 6 F T F nup F F T T First Premise Second Premise m-s T T F F T T T T T F T F st F T T T F T T T Conclusion t~m F row 1 row 2 row 3 row 4 T 7 F T T T T T row 1 row 2 row 3 row 4 row 5 row 6 row 7 row 8 Notice that both premises in rows 2, 6, 7,and 8 are true where all conclusions are also true. This means that the argument is valid.
Transcribed Image Text:Example 4.2 Use truth table to determine whether the argument is valid or invalid. 1. If it rains, then the game will not be played. It is not raining. Therefore, the game will be played. Solution: Let r represents "it rains" and g represents "the game will be played". The symbolic form of the argument will be: r-g Ag Now let us construct truth table. r Solution: Label each simple statement. T T F F m-s s t -t-~m m T T T Construct truth table. T F Notice on the preceding table that row 4, where both premises are true, produced false conclusion. This is enough to say that the argument is invalid. m: I am going to run the marathon s: I will buy new shoes. t: I will buy a television. The symbolic form of the argument is: F 2. If I am going to run the marathon, then I will buy new shoes. If I buy new shoes, I will not buy a television. Therefore If I buy a television, I will not run the marathon. F F F S T T F F 8 T F T F T T F F t T F T F = First Premise Second Premise Conclusion R T r~g F T T T 6 F T F nup F F T T First Premise Second Premise m-s T T F F T T T T T F T F st F T T T F T T T Conclusion t~m F row 1 row 2 row 3 row 4 T 7 F T T T T T row 1 row 2 row 3 row 4 row 5 row 6 row 7 row 8 Notice that both premises in rows 2, 6, 7,and 8 are true where all conclusions are also true. This means that the argument is valid.
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