1. SOLVING VENN DIAGRAMS www.mathxtc.com

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

3. SOLVING VENN DIAGRAMS www.mathxtc.com Method 1: Algebraic Approach

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

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

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

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

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

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

10. 10 - x 11 - x16 - x ab c

11. a + 10 + (16 – x) = 25 x - 1ab c  a = x – 1

12. a + 10 + (16 – x) = 25 x + 13b c  a = x – 1 b + 10 + (11 – x) = 34  b = x + 13

13. 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

14. 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

15. SOLVING VENN DIAGRAMS www.mathxtc.com Method 2: Trial and Adjustment Approach

16. Here is the given information: Find:

18. Try x = 4 ? Needs to be 74

19. Now Try x = 7 ? Bingo !!! x = 7 74 – 71 = 3 and 4 + 3 = 7 Is this a coincidence?

20. SOLVING VENN DIAGRAMS www.mathxtc.com Method 3: Reasoning Approach

21. Here is the given information: Find:

22. 25 + 34 + 37 = 96 Find: A + B + C = 66 96 – 66 = 30 Surplus 10 + 16 + 11 = 37 37 – 30 = 7 Surplus 7 = 7