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SOLVING VENN DIAGRAMS. www.mathxtc.com. The universal Set, U, and the sets A, B and Contained within it are such that:. Find:. SOLVING VENN DIAGRAMS. Method 1: Algebraic Approach. www.mathxtc.com. The universal Set, U, and the sets A, B and Contained within it are such that:. Find:. - PowerPoint PPT Presentation
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The universal Set, U, and the sets A, B and Contained within it are such that:
8)(16)(11)(10)(
CBAnCAnCBnBAn
37)(34)(25)(74)(
CnBnAnUn
)( CBAn Find:
The universal Set, U, and the sets A, B and Contained within it are such that:
8)(16)(11)(10)(
CBAnCAnCBnBAn
)( CBAn
37)(34)(25)(74)(
CnBnAnUn
Find:
A B
C
The universal Set, U, and the sets A, B and Contained within it are such that:
8)(16)(11)(10)(
CBAnCAnCBnBAn
)( CBAn
37)(34)(25)(74)(
CnBnAnUn
Find:
74
A B
C
The universal Set, U, and the sets A, B and Contained within it are such that:
8)(16)(11)(10)(
CBAnCAnCBnBAn
)( CBAn
37)(34)(25)(74)(
CnBnAnUn
Find:
25 34
37
74
A B
C
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)(
CBAnCAnCBnBAn
)( CBAn Find:
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)(
CBAnCAnCBnBAn
)( CBAn Find:
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)(
CBAnCAnCBnBAn
)( CBAn Find:
25 34
37
10
16 11
x
8
74
A B
C
10 - x
11 - x16 - x
a b
c
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
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
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 – 859 + x = 66 x = 7
7)( CBAn
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 – 859 + x = 66 x = 7
7)( CBAn
SOLVINGVENN DIAGRAMS
www.mathxtc.com
Method 2: Trial and Adjustment
Approach
25 34
37
10
16 11
8
74
A B
C
Here is the given information:
)( CBAn Find:
25 34
37
10
16 11
8
74
A B
C
10)( CBAn
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
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?
25 34
37
10
16 11
8
74
A B
C
Here is the given information:
)( CBAn Find:
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
