Matrix Logic

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Chapter 4 Matrix Logic
A matrix, or two-dimensional chart helps organize
information in a useful way and facilitates
eliminating possibilities, which is an important
strategy for solving logic problems.
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This table shows what classes are offered at each
period in River High School.
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Example 1. Ted, Ken, Allyson, and Janie (two
married couples) each has a favorite sport. The
sports are running, swimming, biking, and golf.
Determine from the following clues who likes
which sport.

• Ted hates golf he agrees with Mark Twain that
  golf is a good walk spoiled.
• Ken cant run around the block, and neither can
  his wife.
• Each womans favorite sport is featured in a
  triathlon.
• Allyson bought her husband a new bike for his
  birthday for use in his favorite sport.

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Example 2. Outdoor Barbecue Tom, John,
Fred, and Bill are friends whose occupations are
(in no particular order) nurse, secretary,
teacher, and pilot. They attended a
church picnic
recently,
and each one brought
his favorite meat
(hamburger, chicken,
steak,
and hot dogs).
From the clues below,
determine each mans
name,
occupation, and
favorite meat.
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Names
Occupations
Favorite meats
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Clues

• Tom is neither the nurse nor the teacher.
• Fred and the pilot play golf together. The burger
  lover and the teacher hate golf.
• Tom brought hot dogs.
• Bill sat next to the burger fan and across from
  the steak lover.
• The secretary hates golf too.

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Example 3 College Applications Four high school
friends (one is named Cathy) are about to go to
college. Their last names are Williams, Burbank,
Collins, and Gunderson. Each is enrolled in a
different college (one is a state college). From
the clues below, determine each persons full
name and the college he or she will attend.
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Clues

• No students first name begins with the same
  first letter as his or her last name. No
  students first name ends with the same last
  letter of his or her last name.
• Neither Hank nor Williams is going to the
  community college.
• Alan, Collins, and the student who is going to
  the university all live on the same street. The
  other student lives two blocks away.
• Gladys and Hank live next door to each other.
• The private college accepted Hanks application,
  but he decided he couldnt afford to go.