Page 750 - Basic College Mathematics with Early Integers

726 A PPEND I X C I INDUCTIVE AND DEDUCTIVE REASONING

Sometimes a grid may be useful in organizing information.

PRACTICE 6 Example 6 Max, Jim, Michael, and Dong Ming have careers as an accoun-
Persons A, B, C, and D sit in the tant, a mathematician, a computer programmer, and a manager,
front row of their mathematics not necessarily in the given order. Use the statements below to
class. Use the statements below determine which person is the mathematician.
to determine their order. 1. Jim and Max went to lunch with the mathematician.
1. Person D is sitting between 2. The accountant and the computer programmer taught Jim in college.
persons A and B.
3. Max and Dong Ming went to Florida with the computer programmer.
2. Person C is sitting next to
person B only. Solution: Draw a grid to organize the information.Then record the information
3. Person C is not on the far given in each statement. From statement 1, we know that both Jim and Max are
left. not the mathematician. To indicate this on the grid, place X’s in the appropriate
places. (See below on the left.)

math. comp. prog. acct. manager math. comp. prog. acct. manager
Jim X Jim X X X
Max X Max X
Michael Michael
Dong Ming Dong Ming

From statement 2, we know Jim is not the accountant and he is not the computer
programmer, so place an X in the grid corresponding to Jim/accountant and an X
in the grid corresponding to Jim/computer programmer. (See above on the right.)
At this point, notice that Jim must be the manager. Place a check mark in the
grid corresponding to Jim/manager. Since Jim is the manager, no one else is and
we can place X’s in the rest of the manager column to indicate that no one else is
the manager. (See below on the left.)

math. comp. prog. acct. manager math. comp. prog. acct. manager
Jim X X X ✓ Jim X X X ✓
Max X X Max X X X
Michael X Michael X
Dong Ming X Dong Ming X X

From statement 3, we know Max and Dong Ming are not the computer
programmer. Record this information in the grid. (See above on the right.) Notice
that Max must be the accountant. Place a check mark in the grid under
Max/accountant and mark the rest of that column with X’s. (See below on the
left.) Now Dong Ming must be the mathematician and Michael must be the
computer programmer. (See below on the right.)

math. comp. prog. acct. manager math. comp. prog. acct. manager
Jim X X X ✓ Jim X X X ✓
Copyright 2012 Pearson Education, Inc.
Max X X ✓ X Max X X ✓ X
Michael X X Michael X ✓ X X
Dong Ming X X X Dong Ming ✓ X X X

Work Practice 6

Answer
6. A, D, B, C