Exam 3: The Nature of Logic

Write the inverse of the given statement. ​ If I brush my teeth with Smiles toothpaste, then I will have fewer cavities. ​

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

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

Translate the following statement into symbols. ​ Dinner includes soup and salad, or the vegetable of the day. ​ Use p for soup, d for salad, and v for vegetable. Please enter parentheses to indicate the order of operations.

Alfie, Betty, and Connie are the members of a Senate committee. Design a circuit that will output yea or nay depending on the way the majority of the committee members voted. Let the committee members be a, b, and c, respectively. ​ (a) (b) (c) ​

Find a so that the statement is true. ​ ​

Find a so that the statement is true.

Fill in the blank with a symbolic statement that follows from the given statement. The applicant for the position must have a two-year college degree in drafting or five years of experience in the field. Let a: You are an applicant for the position. q: You are qualified for the position. e: You have a two-year college degree in drafting. f: You have five years of experience in the field. ​

Suppose you are given 12 coins, one of which is counterfeit and weighs a little more or less than the real coins. Using a two-pan balance scale, what is the minimum number of weighings necessary to find the counterfeit coin? ​

Construct a truth table for the given statement ​

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

Form a valid conclusion, using all the statements for each argument. Give reasons. ​ If we go to the ballet, then we are enlightened. We are not enlightened. ​ We __________ (go, do not go) to the ballet. __________ (direct, indirect)

Find a so that the statement is true.

Let p : Prices will rise; q : Taxes will rise. Translate the following statement into symbols. ​ Prices will rise, or taxes will not rise.

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, Annie, and Nancy. 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. Annie : I have two plums. Nancy : 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? ​

Write the negation of the compound statement ​ ​

Construct a truth table for the given statement. ​ ​

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

A fox, hunting for a morsel of food, spotted a huge bear about 200 yards due east of him. Before the hunter could become the hunted, the crafty fox ran due north for 200 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. ​ The color of the bear was __________.

Write the negation of the compound statement. ​ , if and . ​