Sets and Venn Diagrams (B) Worksheet | Printable Maths Worksheets - Free Printable

Here is the step-by-step solution to the problems on the worksheet.

Section A

Left Diagram (Numbers)
* Set A contains: {1, 3, 7, 11, 2, 14}
* Set B contains: {2, 14, 5, 9, 20, 13}
* Outside the circles contains: {0, 17}

1. $A \cap B$ (Intersection of A and B): These are the numbers inside both circles (the overlap).
* Answer: {2, 14}
2. $A' \cup B$ (Not A union B): "Not A" means everything outside of circle A. "Union B" means add everything inside circle B.
* "Not A" includes: {0, 17} (outside) and {5, 9, 20, 13} (inside B only).
* "B" includes: {2, 14, 5, 9, 20, 13}.
* Combining these gives: {0, 17, 5, 9, 20, 13, 2, 14}.
* Answer: {0, 2, 5, 9, 13, 14, 17, 20}
3. $(A \cap B)'$ (Not intersection of A and B): This is everything *except* the overlap.
* The overlap is {2, 14}.
* Everything else is: {0, 17, 1, 3, 7, 11, 5, 9, 20, 13}.
* Answer: {0, 1, 3, 5, 7, 9, 11, 13, 17, 20}

Right Diagram (Letters)
* Set A contains: {f, z, e, i, b}
* Set B contains: {z, p, r, m, e, h}
* Set C contains: {i, b, e, h, g}
* Outside contains: {s, d, c, k, j}

1. $A =$ List all letters inside circle A.
* Answer: {f, z, e, i, b}
2. $B' =$ List all letters NOT inside circle B.
* This includes everything outside B (s, d, c, f, i, b, g, k, j).
* Answer: {s, d, c, f, i, b, g, k, j}
3. $A \cap B \cap C =$ List letters inside all three circles (the very center).
* Answer: {e}

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Section B

Holiday 1 (Left Side)
* Camping Only: 11
* Both Camping and Fishing: 5
* Fishing Only: 8
* Neither: 24

1. How many travellers chose camping?
* Add those who did camping only and those who did both.
* $11 + 5 = 16$
2. How many travellers did not choose fishing?
* Add those who did camping only and those who did neither.
* $11 + 24 = 35$
3. How many travellers did not choose camping or fishing?
* This is the number outside the circles.
* Answer: 24
4. How many travellers only chose fishing?
* This is the number in the "Fishing" circle that doesn't overlap.
* Answer: 8

Holiday 2 (Right Side)
* Camping Only: 10
* Fishing Only: 3
* Water Sports Only: 18
* Camping & Fishing only: 1
* Camping & Water Sports only: 6
* Fishing & Water Sports only: 1
* All three: 2
* None: 9

1. How many travellers are on Holiday 2?
* Add every number in the box.
* $10 + 1 + 3 + 6 + 2 + 1 + 18 + 9 = 50$
* Answer: 50
2. What is the probability that a traveller chooses camping, fishing and water sports?
* Look for the center number (all three): 2.
* Divide by the total number of travellers: 50.
* $2/50$ or $1/25$ (which is 0.04).
* Answer: 0.04 (or 4%)
3. Work out $P((C \cup W)')$
* $C \cup W$ means "Camping OR Water Sports".
* $(C \cup W)'$ means "NOT (Camping OR Water Sports)". This is the complement.
* The only people who fit this description are those who did Fishing ONLY.
* The number for Fishing Only is 3.
* Probability = $3/50 = 0.06$.
* Answer: 0.06
4. Work out $P(C \cup W')$
* $W'$ means "Not Water Sports".
* $C \cup W'$ means "Camping OR Not Water Sports".
* Let's count the people who fit this:
* Camping Only (10) - Yes (It's Camping)
* Camping & Fishing (1) - Yes (It's Camping)
* Fishing Only (3) - Yes (It's Not Water Sports)
* None (9) - Yes (It's Not Water Sports)
* *Check exclusions:* Camping & Water (6) - No (It's Water Sports, not Camping). All Three (2) - No (It's Water Sports, not Camping). Fishing & Water (1) - No (It's Water Sports).
* Total count: $10 + 1 + 3 + 9 = 23$.
* Probability = $23/50 = 0.46$.
* Answer: 0.46

Final Answer:
Section A (Left)
$A \cap B = \{2, 14\}$
$A' \cup B = \{0, 2, 5, 9, 13, 14, 17, 20\}$
$(A \cap B)' = \{0, 1, 3, 5, 7, 9, 11, 13, 17, 20\}$

Section A (Right)
$A = \{f, z, e, i, b\}$
$B' = \{s, d, c, f, i, b, g, k, j\}$
$A \cap B \cap C = \{e\}$

Section B (Holiday 1)
1) 16
2) 35
3) 24
4) 8

Section B (Holiday 2)
1) 50
2) 0.04
3) 0.06
4) 0.46