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SOLVING VENN DIAGRAMS www.mathxtc. com

Solving Venn Diagrams

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• SOLVING VENN DIAGRAMSwww.mathxtc.com

• The universal Set, U, and the sets A, B and Contained within it are such that:Find:

• SOLVING VENN DIAGRAMSwww.mathxtc.com

Method 1: Algebraic Approach

• The universal Set, U, and the sets A, B and Contained within it are such that:Find:

• The universal Set, U, and the sets A, B and Contained within it are such that:Find:

• The universal Set, U, and the sets A, B and Contained within it are such that:Find:

• The universal Set, U, and the sets A, B and Contained within it are such that:Find:

• The universal Set, U, and the sets A, B and Contained within it are such that:Find:

• The universal Set, U, and the sets A, B and Contained within it are such that:Find:

• 10 - x11 - x16 - xabc

• a + 10 + (16 x) = 25x - 1abc a = x 1

• a + 10 + (16 x) = 25x + 13bc a = x 1b + 10 + (11 x) = 34 b = x + 13

• a + 10 + (16 x) = 25 a = x 1b + 10 + (11 x) = 34 b = x + 1337 + (x 1) + (10 x) + (x + 13) = 74 859 + x = 66 x = 7

• a + 10 + (16 x) = 25 a = x 1b + 10 + (11 x) = 34 b = x + 1337 + (x 1) + (10 x) + (x + 13) = 74 859 + x = 66 x = 7

• SOLVING VENN DIAGRAMSwww.mathxtc.com

Method 2: Trial and Adjustment Approach

• Here is the given information:Find:

• Try x = 4 ?Needs to be 74

• Now Try x = 7 ?Bingo !!!x = 774 71 = 3 and4 + 3 = 7Is this a coincidence?

• SOLVING VENN DIAGRAMSwww.mathxtc.com

Method 3: Reasoning Approach

• Here is the given information:Find:

• 25 + 34 + 37 = 96Find:A + B + C = 6696 66 = 30 Surplus10 + 16 + 11 = 3737 30 = 7 Surplus7= 7