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 TOPICS This page:   logic    Search   Dr. Math See also the Dr. Math FAQ:   false proofs,   classic fallacies and   liars, truthtellers and   proofs Internet Library:   logic MIDDLE SCHOOL About Math Algebra    equations    factoring expressions    graphing equations Arithmetic    division    exponents    factorials    factoring numbers    fractions/percents    logarithms Definitions Geometry    2-dimensional      conic sections/        circles      triangles/polygons    3D and higher      polyhedra History/Biography Logic Measurement    calendars/      dates/time    temperature    terms/units Number Sense    factoring numbers    negative numbers    pi    prime numbers    square roots Probability Puzzles Ratio/Proportion Statistics Word Problems Browse Middle School Logic Stars indicate particularly interesting answers or good places to begin browsing. 8th Grade Logic [12/15/1994] Why in a conditional statement if the "p" in the hypothesis is false, is the entire statement then true? Why isn't it undecided? Why do you use the symbols p and q for logic statements? Derfs and Enajs: Algebra and Venn Diagrams [03/09/2003] All Derfs are Enajs. One-third of all Enajs are Derfs. Half of all Sivads are Enajs. One Sivad is a Derf. Eight Sivads are Enajs. The number of Enajs is 90. How many Enajs are neither Derfs nor Sivads? Farmer Crossing a River [09/24/2001] A farmer is taking his prize lettuce, lion, llama, and pet leviathan (a unique creature that eats llamas and lions unless a lettuce is present) to market... Finding One Coin of 12 in 3 Steps [8/6/1996] Given a pile of twelve coins of equal size with one of a different weight, in three weighings find the unequal coin... Intersection of Sets [10/02/2000] I do not understand intersection of sets. Can you give me an example? Logic: Definitions [04/04/2000] What does deductive reasoning mean? What does inductive reasoning mean? Lucky Seven Fractions Puzzle [12/22/2001] Put numbers 1-9 in order to make the equation correct: XX/XXX+XX/XX=7. Math Logic [6/5/1996] Sally, Ron, Jim, and Meghan are President, VP, Treasurer, and Captain of the cheerleading squad, but not necessarily in that order. Who is what? Negation in Logic [8/3/1996] What is the negation of "In every village, there is a person who knows everybody else in that village"? Steps and Footprints [5/31/1996] Four friends were racing down a dusty staircase... how many steps had just one person's footprints? What Color Hat am I Wearing? [4/17/1996] Three students close their eyes, and the teacher puts a hat on each of their heads (hiding the other two hats)... What is Fuzzy Logic? [10/29/2000] I need a simple definition of fuzzy logic and what it's used for. Who Owns the Zebra? [08/05/1997] I have tackled this indirect reasoning problem and have come up with a solution that I am not sure is correct. Who Stole Second Base? [2/20/1995] The umpire was convinced that either Archie, Buster, Cal, or Dusty had stolen second base. Each player, in turn, made a statement, but only one of the four statements was true. Who told the truth? 100 Birds for 100 Dollars [03/19/1998] Blue birds cost \$10, green birds \$3, and yellow birds 50 cents... Age of Children [02/11/1997] There are three kids. The product of their ages is 36, the sum of their ages is the house number across the street, and the oldest has red hair. How old are the kids? Ages of Three Children [9/4/1996] During a recent census, a man told the census taker that he had 3 children. When asked their ages, he replied, "The product of their ages is 72..." Alternate Solution Path to Venn Diagram Problem [05/12/2009] There are 30 students in a math class. Twelve belong to the computer club, and eight belong to the photography club. Three belong to both clubs. How many belong to neither club? Arranging Numbers [06/26/2002] Arrange the numbers 1-8 into the given configuration such that consecutive numbers are never adjacent. Census Taker [02/20/2002] The census taker says, "I need to know the ages of your children." Claim the Last Flag [10/25/2002] Two teams face 21 flags. Teams take turns choosing 1, 2, or 3 flags at each turn. The team that can claim the last flag wins. Concept of Farmer Crossing a River [04/30/2002] What concept does the farmer, fox, and chicken problem use, and how does it relate to the sheriffs and outlaws problem, husband and wives problem, and missionaries and cannibals problem? Criminal Logic Problem [02/19/2005] A challenging logic problem involving five criminals charged with five crimes. The names of the criminals are the same as the crimes, but no criminal commited the crime of his name. Using several clues, determine who committed murder. Crossing a River: Cannibals and Missionaries [10/15/2001] Three missionaries and three cannibals wish to cross a river using a single boat that will hold only two people. If at any time the cannibals outnumber the missionaries, those missionaries will be eaten... Crossing the Desert [05/22/2001] A truck gets one mile per gallon, and can hold 400 gallons at a time. How much is the minimum amount to cross a 1000-mile desert? Defining Multiplication [08/16/2002] What is the distinction between 3*4 and 4*3? Diagram for Math Numbers [10/05/1997] My daughter is doing a tree diagram using terms related to math "numbers." Could you please explain in lay terms what surds are? The Difference between And and Or [01/23/2008] There are 3 knives, 4 spoons, and 4 forks on a table. What fraction of the utensils are spoons OR forks? I think it should be 4/11 but the answer is 8/11. Can you explain why? Distributing 'Not' over a Conjunction [09/18/2003] When 'It is not true that...' appears in front of a conjunction, does it apply to both conjuncts, or only the first one? Examples of Logical Paradoxes [03/14/2006] What kind of logic statement is "I am telling you the truth when I say I am a liar"? Farmer, Goat, Wolf, and Cabbage Cross a River [03/13/1998] Fewest number of trips a farmer can make to get a goat, wolf, and cabbage across a river. The Four Doors of Xanth [02/11/1998] Each door conceals one item: a treasure, a rope, a key, and a lantern. You must find all four items in a particular order to keep the treasure. How Many are in the Group? [10/17/1996] Everyone in the group had been to at least one of the parks... How Many Pieces of Candy in Each Jar? [09/30/1997] At the annual Cumberland County fair, one of the more popular booths is the Candy Contest... Inclusion-Exclusion Principle [09/03/2002] In a survey of 100 people, 85 like calypso and 93 like pan. Calculate the number of people who like both calyso and pan. Interpreting Intersections [07/09/2002] Out of 100 people, 10 drink Coke, 15 drink Sprite, and 20 drink Pepsi. How many drink both Coke and Pepsi at the same time? Coke and Sprite? Pepsi and Sprite? All three? Introduction to Logic and Truth Tables [09/27/2000] I can't figure out the p and q thing. Can you explain what they are and how operations like "AND" work? Is Henry Guilty? (Geometry Puzzle) [6/10/1996] In Hughmoar County, residents shall be allowed to build a straight road between two homes as long as the new road is not perpendicular to any existing county road... Is It Possible That x/0 is Not Really Undefined? [06/14/2004] Is it possible that 1/0 is not really undefined, but is in fact the key to a whole new class of numbers, much as the imaginary unit i led to the development of complex numbers? John Venn and Venn Diagrams [09/04/1998] Can you give me some information on John Venn and the origin of Venn diagrams? 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