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Very often in math we need to use reasoning
to solve problems. We call this study of reasoning, the "Language
of Logic". It deals with statements that are either
true or
false. When trying to
determine the truth value of a compound statement, first find the
truth value (true or
false) of each part of the statement. OK, that's too many
words! Let's look at some examples!
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John, Joe, Cari, and Alan like to
draw. One of them likes working with colored markers best,
another with watercolor paints, another with colored chalk and
another with colored pencils. The following are your
clues.
#1: John does not
like to work with paintbrushes.
#2: Joe
likes to sharpen his drawing tools.
#3: Cari and
Alan do not like dust.
#4: Alan
sometimes gets bristles in his art work.
Find out what each child likes
best. |
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Are you confused?
Don't know where to start? Here is a useful tool to find
who likes to draw with what!
It's called a
LOGIC GRID,
which is a grid of rows and columns used to organize information
in a problem. It allows you to find out what is true
and what is false. |
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First set up
the table with drawing material choices across the top and the
kids' names along the side. Then put NO in the cells that are
certain not to be the choice for that person according to the
clues given. |
| |
Colored Markers |
Watercolor Paints |
Colored Chalk |
Colored Pencils |
| Joe |
|
NO (b/c of
#1) |
|
|
| John |
NO (b/c of
#2) |
NO (b/c of
#2) |
NO (b/c of
#2) |
|
| Cari |
|
|
NO (b/c of
#3) |
|
| Alan |
|
|
NO (b/c of
#3) |
|
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Then start choosing YES when three
of the four possible answers are NO.
|
| |
Colored Markers |
Watercolor Paints |
Colored Chalk |
Colored Pencils |
| Joe |
|
NO (b/c of #1) |
YES (only
one left in column)) |
|
| John |
NO (b/c of #2) |
NO (b/c of #2) |
NO (b/c of #2) |
YES (only
one left in row) |
| Cari |
YES (b/c
all the others are "used") |
|
NO (b/c of #3) |
|
| Alan |
|
YES (b/c
of#4) |
NO (b/c of #3) |
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Do you understand why Cari had to be the
one who liked Colored Markers best? Because Joe used colored chalk, John
used colored pencils, and Alan used Watercolor Paints, Cari was left
with to Colored Markers.
Remember,
when faced with a "Logic" problem, try to set up a Logic Grid!
Ready
for Practice?
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