Exam 3: The Nature of Logic

Form a valid conclusion, using all the statements for each argument. Give reasons. ​ If we go to the theater, then we are enlightened. We are not enlightened.

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. ​ If a² is odd, then a must be odd. a is even. Therefore, a² is even. Assume that if a number is even, then it is not odd.

Write the inverse of the given statement. ​ ​

Daniel Kilraine was killed on a lonely road, two miles from Pontiac, at 3:30 A.M. on March 3, 1997. Henry, Curly, Slim, Mickey, and The Kid were arrested a week later in Detroit and questioned. Each of the five made four statements, three of which were true and one of which was false. One of these men killed Kilraine. Who dunit? Their statements were: Henry : "I was in Chicago when Kilraine was murdered. I never killed anyone. The Kid is the guilty man. Mickey and I are pals." Curly : "I did not kill Kilraine. I never owned a revolver in my life. The Kid knows me. I was in Detroit the night of March 3rd." Slim : "Curly lied when he said he never owned a revolver. The murder was committed on March 3rd. One of us is guilty. Henry was in Chicago at the time." Mickey : "I did not kill Kilraine. The Kid has never been in Pontiac. I never saw Henry before. Curly was in Detroit with me on the night of March 3rd." The Kid : "I did not kill Kilraine. I have never been in Pontiac. I never saw Curly before. Henry lied when he said I am guilty." __________ committed the murder.

Determine whether the argument in the problem below is valid or invalid. If valid, name the type of reasoning and if invalid, determine the error in reasoning. ​ If , then . Therfore, .

Write the negation of the compound statement ​ ​ Please enter the sign ∩ for "and", and the sign ∪ for "or". Do not add commas in your answer.

Determine the truth value of the given statement. ​ ​ either p or q

Find a so that the statement is true. a = __________

Suppose I have three bags, one with two peaches, another with two plums, and a third mixed bag with one peach and one plum. Now I give the bags (in mixed-up order) to Alice, Betty, and Connie. I tell the three to look into their bags and that I want each to make a statement about the contents of her bag, but I want them to lie. Here is what they say: ​ Alice : I have two peaches. Betty : I have two plums. Connie : I have one peach and one plum. ​ Now here is the game. I want you to develop a strategy of asking one of the three to reach into their bag and pull out one fruit and show it to you. The fruit is then returned to the bag and you ask another to do the same thing. Continue until you can deduce which bag is the mixed bag. What is the minimum possible number of necessary moves? Explain.

Choose a valid conclusion, using all the statements for each argument. ​ Children are illogical. Nobody is despised who can manage a crocodile0. Illogical persons are despised. Children can manage crocodiles 0 Children can't mange crocodiles 0 Everybody can manage crocodiles 0

Assume p is T, q is F, and ​r is F. Find the truth value for the compound statement. ​

Is the following example a statement? Answer yes or no. ​ Division by zero is impossible.

Write the negation of the compound statement. ​ ​

Write the negation of the compound statement. ​ If x + 3 = 11, then x = 8. ​

Translate the statement into symbols. ​ To obtain the loan, I must have an income of $85,000 per year. Let ​ K: I must have an income of $85,000 per year L: Obtaining the loan

Explain when the light on a circuit is off. ​

What does the circuit symbol in the figure mean? ​ ​

I have a habit of getting up before the sun rises. My socks are all mixed up in the drawer, which contains 8 blue and 18 grey socks. I reach into the drawer and grab some socks in the dark. How many socks do I need to take from the drawer to be sure that I have a matched pair? ​ __________ socks

Find a so that the statement is true. a = __________

The figure shows some faces from the "Guess Who?" game. Decide whether the statement is true or false. ​ There is one face that has glasses. ​