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Logic

For numbers 1 through 7, draw a Venn Diagram to determine the validity of the argument. Then write VALID or INVALID. (4 points each)
  1. All master photographers are artists. Ansel Adams is a master photographer. Therefore, Ansel Adams is an artist. Kristi Yamaguchi on ice

  2. All Olympic gold medal winners are role models. Kristi Yamaguchi is a role model. Therefore, Kristi Yamaguchi is an Olympic gold medal winner.

  3. All homeless people are unemployed. Jack is not a homeless person. Therefore, Jack is not unemployed.

  4. All motorcycle riders are outlaws. Evil Kneivel is not an outlaw. Therefore, Evil Kneivel is not a motorcycle rider.

  5. All pesticides are harmful to the environment. No fertilizer is a pesticide. Therefore, no fertilizer is harmful to the environment.

  6. No one who can afford health insurance is unemployed. All politicians can afford health insurance. Therefore, no politician is unemployed.

  7. No professor is a millionaire. No millionaire is illiterate. Therefore, no professor is illiterate.

  8. Find the negation to each statement. (6 points)
    1. Her dress is not red.
    2. All dogs have four legs.
    3. No plan is foolproof.
    4. Some computers are priced under $100.
    5. The car is white or the car is black.
    6. If the sun is shining, then it is warm.

  9. Write the CONVERSE, INVERSE, and CONTRAPOSITIVE of each conditional statement. (6 points)
    1. If it is raining then the streets are wet.
    2. If you have not studied then you will not pass.

    Solve each logic problem and give a full explanation of your answer.

  10. High School Athletes

    Three high school girls each participate in a different sport. From the following statements, determine the full name of each girl, and the sport each one plays. Give a logical argument verifying your answer. (5 points)

    First Names: Last Names: Sports:
    Amy Dean Soccer
    Bridget Evans Tennis
    Christine Frost Volleyball

    1. Neither Amy nor Miss Dean ever plays tennis.
    2. Bridget plays soccer.
    3. Miss Frost plays volleyball.

  11. Three Suspects
    You are a detective trying to solve a murder case. You have determined that the killer is one of three suspects. The only thing you know about the suspects is that one is a truthteller (always tells the truth), one is a liar (always lies), and one schizophrenic (alternates between truths and lies). Each suspect makes two statements:
    Suspect A: "I am a schizophrenic. Suspect B is innocent."
    Suspect B: "I am a truthteller. Suspect C is innocent."
    Suspect C: "I am a liar. Suspect A is innocent."

    Who is the killer? Give a logical argument supporting your answer. (10 points)

  12. Who Loves Who?
    Four men and four women are shipwrecked on a deserted island. Each person falls in love with one person and is loved by one person.

    Chad loves the girl who loves David.
    Arthur loves the girl who loves the man who loves Ellen.
    Bruce loves the girl who loves the man who loves Fannie.
    Gloria does not love Bruce.
    Hazel loves a man who does not love Gloria.

    Given the above information, determine and explain using a logical argument who loves who. (10 points)

  13. The Hat Game
    Jack, Kevin, and Sally are playing a game called The Hat Game. They sit in a circle facing each other and a judge places a white or black hat on each of their heads. When the judge says "GO," all players who see a black hat must raise their hands. The first player to deduce the color of his or her own hat wins the game. Now, the judge put a black hat on each player’s head and said, "GO." After a few moments, Sally knew her hat was black. How did she deduce this? (15 points)

    The completed answer to #14 requires approximately one page of writing.

  14. The Soccer Tournament
    Eight soccer teams from the Pee Wee division competed in a single elimination tournament. The teams were the Arrows, the Blazers, the Crickets, the Daisies, the Eagles, the Frogs, the Gladiators, and the Hippos. Use the following clues to figure out the winner of the tournament. Then give a logical argument to explain why no other team could have won. (20 points)
    1. There were no tie games in the tournament.
    2. There were a total of 26 goals scored in the tournament.
    3. No two games had the same score. The score of the final game was 4-2.
    4. No team scored the same number of goals in two different games.
    5. The Blazers made a roaring start, beating the Hippos in their first game by 3 goals.
    6. The Daisies played the Gladiators in the first round. The Gladiators scored two goals in that game.
    7. The Arrows played the Frogs in the second round. The game was close and the final score differed by only a goal.
    8. Each team scored at least one goal in the tournament.

BONUS QUESTION: The Door to Heaven
You are standing in a room with two doors. One door leads to heaven and the other leads to hell but you do not know which is which. There are two guardians with you in the room. One of the guardians always tells the truth and the other always lies, but again you do not know which is which. You are allowed to ask one of the guardians one question. What question should you ask to be assured that the door you choose will be the door that leads to heaven? (5 points)

 
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