SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such...
Transcript of SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such...
![Page 2: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/2.jpg)
The universal Set, U, and the sets A, B and Contained within it are such that:
8)(
16)(
11)(
10)(
CBAn
CAn
CBn
BAn
37)(
34)(
25)(
74)(
Cn
Bn
An
Un
)( CBAn Find:
![Page 4: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/4.jpg)
The universal Set, U, and the sets A, B and Contained within it are such that:
8)(
16)(
11)(
10)(
CBAn
CAn
CBn
BAn
)( CBAn
37)(
34)(
25)(
74)(
Cn
Bn
An
Un
Find:
A B
C
![Page 5: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/5.jpg)
The universal Set, U, and the sets A, B and Contained within it are such that:
8)(
16)(
11)(
10)(
CBAn
CAn
CBn
BAn
)( CBAn
37)(
34)(
25)(
74)(
Cn
Bn
An
Un
Find:
74
A B
C
![Page 6: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/6.jpg)
The universal Set, U, and the sets A, B and Contained within it are such that:
8)(
16)(
11)(
10)(
CBAn
CAn
CBn
BAn
)( CBAn
37)(
34)(
25)(
74)(
Cn
Bn
An
Un
Find:
25 34
37
74
A B
C
![Page 7: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/7.jpg)
25 34
37
10
16 11
74
A B
C
The universal Set, U, and the sets A, B and Contained within it are such that:
8)(
16)(
11)(
10)(
CBAn
CAn
CBn
BAn
)( CBAn Find:
![Page 8: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/8.jpg)
25 34
37
10
16 11
8
74
A B
C
The universal Set, U, and the sets A, B and Contained within it are such that:
8)(
16)(
11)(
10)(
CBAn
CAn
CBn
BAn
)( CBAn Find:
![Page 9: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/9.jpg)
25 34
37
10
16 11
x
8
74
A B
C
The universal Set, U, and the sets A, B and Contained within it are such that:
8)(
16)(
11)(
10)(
CBAn
CAn
CBn
BAn
)( CBAn Find:
![Page 10: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/10.jpg)
25 34
37
10
16 11
x
8
74
A B
C
10 - x
11 - x16 - x
a b
c
![Page 11: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/11.jpg)
25 34
37
10
16 11
10-x
16-x 11-xx
8
74
A B
C
a + 10 + (16 – x) = 25
x - 1a b
c
a = x – 1
![Page 12: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/12.jpg)
25 34
37
x-1
10
16 11
10-x
16-x 11-xx
8
74
A B
C
a + 10 + (16 – x) = 25
x + 13b
c
a = x – 1
b + 10 + (11 – x) = 34
b = x + 13
![Page 13: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/13.jpg)
25 34
37
x-1 x+13
c
10
16 11
10-x
16-x 11-xx
8
74
A B
C
a + 10 + (16 – x) = 25
a = x – 1
b + 10 + (11 – x) = 34
b = x + 13
37 + (x – 1) + (10 – x) + (x + 13) = 74 – 8
59 + x = 66
x = 7
7)( CBAn
![Page 14: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/14.jpg)
25 34
37
6 20
17
10
16 11
3
9 47
8
74
A B
C
a + 10 + (16 – x) = 25
a = x – 1
b + 10 + (11 – x) = 34
b = x + 13
37 + (x – 1) + (10 – x) + (x + 13) = 74 – 8
59 + x = 66
x = 7
7)( CBAn
![Page 15: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/15.jpg)
SOLVINGVENN DIAGRAMS
www.mathxtc.com
Method 2: Trial and Adjustment
Approach
![Page 16: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/16.jpg)
25 34
37
10
16 11
8
74
A B
C
Here is the given information:
)( CBAn Find:
![Page 17: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/17.jpg)
25 34
37
10
16 11
8
74
A B
C
10)( CBAn
![Page 18: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/18.jpg)
25 34
37
10
16 11
8
74
A B
C
71)( Un25 34
37
3 17
14
10
16 11
6
12 74
8
74
A B
C
Try x = 4 ?
Needs to be 74
![Page 19: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/19.jpg)
25 34
37
10
16 11
8
74
A B
C
25 34
37
6 20
17
10
16 11
3
9 47
8
74
A B
C
74)( Un
Now Try x = 7 ?
Bingo !!!
x = 7
74 – 71 = 3 and4 + 3 = 7Is this a coincidence?
![Page 21: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/21.jpg)
25 34
37
10
16 11
8
74
A B
C
Here is the given information:
)( CBAn Find:
![Page 22: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/22.jpg)
25 34
37
10
16 11
8
74
A B
C
25 + 34 + 37 = 96
)( CBAn Find:
A + B + C = 66
96 – 66 = 30 Surplus
10 + 16 + 11 = 37
37 – 30 = 7 Surplus 7
= 7
![Page 23: SOLVING VENN DIAGRAMS . The universal Set, U, and the sets A, B and Contained within it are such that: Find:](https://reader035.fdocuments.in/reader035/viewer/2022062421/56649d945503460f94a7b85a/html5/thumbnails/23.jpg)