4. Given premises "If it does not rain or if it is not foggy, then the sailing race will be heldand the lifesaving demonstration will go on," "If the sailing race is held, then the trophy willbe awarded," and "The trophy was not awarded". Prove the conclusion "It rained." by rules ofinference. You should first represent the premises and the conclusion using logical expressions.

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Answered: 4. Given premises "If it does not rain…

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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Given that the given simple components are propositions presented in the situations of the first column, in the second column write the inference that can be deduced then write what rule have used in the third column. Situation Inference Rule Used 1. Either I shall have a drink or I eat. But, I ate. 2. If I love to eat broccoli then I am a vegetarian. But, I am not a vegetarian. 3. If I will play basketball then I will be sprained. If I will be sprained then I will stay at home.
Translate the following arguments in to symbols and determine which rule of inference shows the argument is valid. p: The date is June 25, 2010. q: The temperature is above 80 degrees. r: It is sunny. If the date is june 25, 2010, then the temperature is above 80 degrees. The date is June 25, 2010. The temperature is above 80 degrees.
Use the rules of inference, show that the given argument is valid or not. The domain is all persons. "You are listening, and I am speaking. If you are listening, then it is not silence. If music system is off then it is silence. If music system is not off then we are in happy mood, imply the conclusion that we are in happy mood and we are good friends.". Give a reason for each step of proof.
Construct a formal proof of validity by adding onlythree statements to the given premises using the rules of inference. Also indicate the number where you based the proof.
A speaks the truth 2 out of 3 times and B 4 vut of 5 times : they agree in the ussertion that from a bag containing 6 halls of different colours, a black hall has heen drawn. Find the probubility that the statement is true.
. a) Using deductive reasoning, simplify the negation of the proposition "If the sun is shining, then I am going to the ball game". Hence, write it in statement form.
If x > 6, then y 7, then y 7, then y < 15. A. Follows logically B. Does not follow logically
Which is the contrapositive of the implication, "If the car has gas, then it will run"? (a) If the car has no gas, then it will not run. (b) If the car will not run, then it has no gas.
Choose what is the conclusion from the following premises: "If I walk under the rain, I get sick" "I take medicine when I am sick." "I did not take medicine"? O O O I walked under the rain I got sick I did not get sick
Answer 2 and 3 in the question. Please make sure the answers are correct. This question is in three parts. Given the premises: If the steak is well done, it’s overcooked. If the steak is overcooked, the fire alarm will go off. Either the batteries have been changed or the fire alarm will not go off. The batteries have only been changed if the ladder is in the room. The ladder is not in the room. Conclude that the steak is not well done. 2. These premises don’t make sense in the real world. Why? 3. How can you change the premises so that they make sense in the real world?
Determine if statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write INVALID
Construct hypotheses based on a given observation and determine if a given scenario is using deductive or inductive reasoning. 5. Chinook, Coho, and sockeye salmon return to the stream where they were hatched to spawn. Therefore, all salmon return to the stream where they were hatched to spawn. What type of logic is represented in the salmon scenario? What is the main caveat for this type of logic? Justify your reasoning.

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