Exam 3: The Nature of Logic

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Choose a valid conclusion, using all the statements for each argument. ​ If we win third prize, we will go to Europe0. If we are ingenious, we will win third prize. We are ingenious. We will go to Europe0 (transitive and direct) We won't go to Europe0 (indirect) We won't win third prize (transitive and direct))

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

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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 I inherit $1,100, I will buy you a cookie. I inherit $1,100. Therefore, I will buy you a cookie. ​

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Form a valid conclusion, using all the statements for each argument. Give reasons. ​ If 2 divides a positive integer N and if N is greater than 2, then N is not a prime number. N is not a prime number.

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

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Four boys were playing marbles; their names were Gary, Henry, John, and Alice. One of the boys had 9 marbles, another had 15, and each of the other two had 12. Their ages were 3, 10, 17, and 18, but not respectively. Gary shot before Henry and Alice. Alice was older than the boy with 15 marbles. Henry had fewer than 15 marbles. Alice shot before Henry. John shot after Henry. If John was 10 years old, he did not have 15 marbles. Gary and Alice together had an even number of marbles. The youngest boy was not the one with 15 marbles. If Henry had 12 marbles, he wasn't the youngest. The 10-year-old shot after the 17-year-old. How old was each boy? ​

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Write the negation of the compound statement. John went to Macy's or Sears. John __________ (did not go, went) to Macy's and he __________ (went, did not go) to Sears.

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

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A fox, hunting for a morsel of food, spotted a huge bear about 175 yards due east of him. Before the hunter could become the hunted, the crafty fox ran due north for 175 yards but then realized the bear had not noticed him. Thus he stopped and remained hidden. At this point the bear was due south of the fox. What was the color of the bear? ​

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

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Form a valid conclusion, using all the statements for each argument. Give reasons. ​ Children are illogical. Nobody is despised who can manage a sport car. Illogical persons are despised.

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

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

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

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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 inherit $1,000, I will buy you a toy . I inherit $1,000. Therefore, I will buy you a toy. ​

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Using gates, design a circuit for the conditional statement. ​ ​ Using gates, design a circuit for the conditional statement. ​ ​   ​ (a)   ​ (b)   ​ (c)   ​ ​ (a) Using gates, design a circuit for the conditional statement. ​ ​   ​ (a)   ​ (b)   ​ (c)   ​ ​ (b) Using gates, design a circuit for the conditional statement. ​ ​   ​ (a)   ​ (b)   ​ (c)   ​ ​ (c) Using gates, design a circuit for the conditional statement. ​ ​   ​ (a)   ​ (b)   ​ (c)   ​

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

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Write the negation of the compound statement. ​ Tim is not here and he is not at home. ​

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Using switches, design a circuit that would find the truth values for the statement. ​ Using switches, design a circuit that would find the truth values for the statement. ​   ​ Select the correct circuit. ​ ​ Select the correct circuit. ​

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Find the negation of the statement. ​ All squares are rectangles. ​

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