Question 1205709
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As it stands right now, <font color=red size=4>this question is incomplete</font>. It is missing 1 key detail. I'll try my best to explain. 


Draw 3 partially overlapping circles with these labels
Y = yam
C = corn
P = plantain
{{{
drawing(400,400,-5,5,-5,5,
line(-4,4,4,4),
line(4,4,4,-4),
line(4,-4,-4,-4),
line(-4,-4,-4,4),

circle(-1,1,2),circle(1,1,2),circle(0,-0.7321,2),

locate(-2.8,2.8,Y),
locate(2.6,2.8,C),
locate(1,-2.6,P),
locate(-2,1.8,a),
locate(0,1.8,b),
locate(2,1.8,c),
locate(-1.5,0,d),
locate(0,0.4,e),
locate(1.2,0,f),
locate(0,-1.5,g),
locate(3,-1.5,h)
)
}}}
Letters 'a' through 'h' indicate the following 
a = yams only
b = yams and corn only (but no plantains)
c = corn only
d = yams and plaintains only (but no corn)
e = all 3 items mentioned
f = corn and plaintains only (but no yams)
g = plantains only
h = none of the 3 items mentioned


Here's the given info
<table border = "1" cellpadding = "5"><tr><td>Number</td><td>Statement</td></tr><tr><td><font color=blue>Fact 1</font></td><td>A group of market women sell at least one of the following items of food stuffs. Yam,corn,and plantain.</td></tr><tr><td><font color=blue>Fact 2</font></td><td>18 of them sell corn</td></tr><tr><td><font color=blue>Fact 3</font></td><td>17 sell yam</td></tr><tr><td><font color=blue>Fact 4</font></td><td>19 sell plantain</td></tr><tr><td><font color=blue>Fact 5</font></td><td>8 sell plantain and corn</td></tr><tr><td><font color=blue>Fact 6</font></td><td>12 sell yam and plantain</td></tr><tr><td><font color=blue>Fact 7</font></td><td>5 sell all the food stuffs</td></tr></table>


<font color=blue>fact 1</font> means that h = 0. 


<font color=blue>fact 7</font> leads to e = 5.


Let's combine <font color=blue>fact 6</font> and <font color=blue>fact 7</font>
12 sell yam and plantain. Five sell all three types, so 12-5 = 7 
Therefore, d = 7



Combine <font color=blue>fact 5</font> and <font color=blue>fact 7</font> to determine that 8-5 = 3 women sell plantain and corn but no yams.
3 goes inside region f
f = 3


Here's what we found so far
d = 7
e = 5
f = 3
h = 0
{{{
drawing(400,400,-5,5,-5,5,
line(-4,4,4,4),
line(4,4,4,-4),
line(4,-4,-4,-4),
line(-4,-4,-4,4),

circle(-1,1,2),circle(1,1,2),circle(0,-0.7321,2),

locate(-2.8,2.8,Y),
locate(2.6,2.8,C),
locate(1,-2.6,P),
locate(-2,1.8,a),
locate(0,1.8,b),
locate(2,1.8,c),
locate(-1.5,0,7),
locate(0,0.4,5),
locate(1.2,0,3),
locate(0,-1.5,g),
locate(3,-1.5,0)
)
}}}
Focus on circle P.


<font color=blue>Fact 4</font> tells us that 19 women sell plantains (some sell other vegetables as well).
The items inside circle P must add to 19.
g+7+5+3 = 19
g+15 = 19
g = 19-15
g = 4
There are 4 women who sell plantains only.


Now focus on circle Y and <font color=blue>fact 3</font>
Because of this given fact, the items in this circle must add to 17.
a+b+7+5 = 17
a+b+12 = 17
a+b = 17-12
a+b = 5


Through similar logic (focus on circle C and <font color=blue>fact 2</font>), you'll find that b+c+5+3 = 18 leads to b+c = 10


We have this system of equations
a+b = 5
b+c = 10
It has 3 variables. Since there are more variables than equations, we do <u>not</u> have enough information to find the numeric value of a,b, nor c.
We need 3 equations to solve for 3 variables.
This is where we come up short.


The general rule for Venn Diagram problems is this: There are 8 regions ('a' through h) so we need 8 given facts of information.
Unfortunately we're only given 7 facts so we're one fact short.
The problem is incomplete. 
Please make sure you didn't miss something to type in, or ask your teacher to see if s/he might have made a typo somewhere.


Refer to these similar Venn Diagram questions to see examples of 8 given facts to help fill out the Venn Diagram.
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