2. in the venn diagram below, circles s, c, and p represent farms raising sheep, cows, and pigs…

2. in the venn diagram below, circles s, c, and p represent farms raising sheep, cows, and pigs, respectively. how many of the 47 farms represented in the diagram do not raise cows? f. 15 g. 17 h. 18 j. 19

2. in the venn diagram below, circles s, c, and p represent farms raising sheep, cows, and pigs, respectively. how many of the 47 farms represented in the diagram do not raise cows? f. 15 g. 17 h. 18 j. 19

Answer

Explanation:

Step1: Identify regions not in circle C

To find farms that do not raise cows, we look at the regions outside circle ( C ). These regions are the parts of circle ( S ) not overlapping with ( C ), the parts of circle ( P ) not overlapping with ( C ), and the overlap of ( S ) and ( P ) not including ( C ).

The regions are:

  • Only ( S ): ( 12 )
  • Only ( P ): ( 5 )
  • Overlap of ( S ) and ( P ) (not ( C )): ( 2 )

Step2: Sum these regions

We add these values together: ( 12 + 5 + 2 ) ( 12 + 5 = 17 ), then ( 17 + 2 = 19 )? Wait, no, wait. Wait, the only ( P ) is ( 5 )? Wait, no, looking at the Venn diagram:

Wait, circle ( P ) has: only ( P ) is ( 5 ), overlap of ( S ) and ( P ) (not ( C )) is ( 2 ), overlap of ( P ) and ( C ) (not ( S )) is ( 4 ), and the triple overlap is ( 1 ). Wait, no, the regions not in ( C ) are:

  • Only ( S ): ( 12 )
  • Overlap of ( S ) and ( P ) (not ( C )): ( 2 )
  • Only ( P ): ( 5 )

Wait, but let's check again. The circle ( C ) has: only ( C ) is ( 10 ), overlap of ( S ) and ( C ) (not ( P )) is ( 13 ), overlap of ( C ) and ( P ) (not ( S )) is ( 4 ), and triple overlap is ( 1 ). So the regions not in ( C ) are:

  • Only ( S ): ( 12 )
  • Overlap ( S \cap P ) (not ( C )): ( 2 )
  • Only ( P ): ( 5 )

Wait, but ( 12 + 2 + 5 = 19 )? But let's check the total number of farms. Let's sum all regions:

Only ( S ): ( 12 ), ( S \cap C ) (not ( P )): ( 13 ), only ( C ): ( 10 ), ( C \cap P ) (not ( S )): ( 4 ), triple overlap: ( 1 ), ( S \cap P ) (not ( C )): ( 2 ), only ( P ): ( 5 ).

Summing all: ( 12 + 13 + 10 + 4 + 1 + 2 + 5 = 47 ), which matches the total. Now, farms not raising cows: regions without ( C ) are ( 12 ) (only ( S )), ( 2 ) ( ( S \cap P ) not ( C ) ), ( 5 ) (only ( P )). So ( 12 + 2 + 5 = 19 )? Wait, but the options have J as 19. Wait, but let's check again. Wait, maybe I made a mistake. Wait, the only ( P ) is ( 5 )? Wait, the circle ( P ) has: the part only ( P ) is ( 5 ), the part ( S \cap P ) (not ( C )) is ( 2 ), the part ( C \cap P ) (not ( S )) is ( 4 ), and the triple overlap is ( 1 ). So total in ( P ) is ( 5 + 2 + 4 + 1 = 12 ). Total in ( S ) is ( 12 + 13 + 2 + 1 = 28 ). Total in ( C ) is ( 13 + 10 + 4 + 1 = 28 ). Total farms: ( 12 + 13 + 10 + 4 + 2 + 5 + 1 = 47 ), correct.

So farms not raising cows: regions not in ( C ) are ( 12 ) (only ( S )) + ( 2 ) ( ( S \cap P ) not ( C ) ) + ( 5 ) (only ( P )) = ( 12 + 2 + 5 = 19 ). Wait, but let's check the options. Option J is 19. Wait, but earlier I thought maybe I messed up, but the calculation gives 19. Wait, but let's re-express:

Regions not in ( C ):

  • Only ( S ): 12
  • ( S \cap P ) (excluding ( C )): 2
  • Only ( P ): 5

Sum: ( 12 + 2 + 5 = 19 ).

Answer:

J. 19