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SOLVING VENN DIAGRAMS www.mathxtc. com

# SOLVING VENN DIAGRAMS

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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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SOLVINGVENN DIAGRAMS

www.mathxtc.com

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:

SOLVINGVENN DIAGRAMS

www.mathxtc.com

Method 1: Algebraic Approach

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

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

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

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:

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:

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:

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 – 8

59 + 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 – 8

59 + x = 66

x = 7

7)( CBAn

SOLVINGVENN DIAGRAMS

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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?

SOLVINGVENN DIAGRAMS

www.mathxtc.com

Method 3: Reasoning 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

25 + 34 + 37 = 96

)( CBAn Find:

A + B + C = 66

96 – 66 = 30 Surplus

10 + 16 + 11 = 37

37 – 30 = 7 Surplus 7

= 7