Sets and Venn Diagrams (A) Worksheet | Printable PDF Worksheets - Free Printable

Here is the complete solution to the worksheet “Sets and Venn Diagrams (A)”, broken down by section.

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## Section A: Correctly list all the data in the sets.

1. Even numbers between 1 and 10

Even numbers are divisible by 2.
Between 1 and 10 (not including 1 and 10? The phrasing “between 1 and 10” usually excludes endpoints, but in math contexts like this, especially with integers, it often includes them unless specified otherwise. However, looking at the context of the rest of the worksheet (e.g., Section B uses {2,4,6,8,10}), we can infer that “between 1 and 10” here means from 2 to 10 inclusive.

✔ So:
Even numbers between 1 and 10 = {2, 4, 6, 8, 10}

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2. Odd numbers between 5 and 15

Odd numbers are not divisible by 2.
“Between 5 and 15” — again, likely inclusive based on context (since 5 and 15 are odd).

So odd numbers: 5, 7, 9, 11, 13, 15

✔ So:
Odd numbers between 5 and 15 = {5, 7, 9, 11, 13, 15}

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## Section B: Sort the data and choose the correct statement below, A, B, or C.

We’ll evaluate each Venn diagram scenario.

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First Venn Diagram: Even and Odd

- Even = {2, 4, 6, 8, 10}
- Odd = {1, 3, 5, 7, 9}

> Union (U) means all elements in either set.

Even ∪ Odd = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Check options:
- A: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} → ✔ Correct
- B: {0} → ✘ Wrong
- C: {1, 2, 5, 8} → ✘ Incomplete

✔ Answer: A

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Second Venn Diagram: Even and Prime

- Even = {2, 4, 6, 8, 10}
- Prime = {2, 3, 5, 7}

> Intersection (∩) means elements common to both sets.

Even ∩ Prime = only number that is both even AND prime → {2}

Check options:
- A: {2, 4, 7} → ✘ 4 and 7 are not in both
- B: {2} → ✔ Correct
- C: {6, 8} → ✘ Neither is prime

✔ Answer: B

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Third Venn Diagram: Even and Square

- Even = {2, 4, 6, 8, 10, 12, 14, 16}
- Square = {4, 9, 16, 25}

> Intersection (∩) = elements common to both sets.

Even ∩ Square = numbers that are both even AND perfect squares → 4 (2²), 16 (4²)

→ {4, 16}

Check options:
- A: {2, 4, 6} → ✘ 2 and 6 are not squares
- B: Even ∪ Square = {4,9,16} → ✘ This is union, not intersection; also incomplete
- C: Even ∩ Square = {4, 16} → ✔ Correct

✔ Answer: C

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## Section C: Chess board and playing cards

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1) Chess Board: Black pieces (B) and Rooks (R)

From the Venn diagram:

- Only Black (not Rook): 14
- Both Black and Rook: 2
- Only Rook (not Black): 2
- Outside both (neither): 14

Total pieces = 14 + 2 + 2 + 14 = 32 (which makes sense for a chessboard).

#### 1) How many pieces are black and rooks?
This is the intersection: B ∩ R = 2

✔ Answer: 2

#### 2) Describe B ∪ R in words.
B ∪ R = All pieces that are either black OR rooks OR both.

✔ Answer: The set of all pieces that are black or rooks or both.

#### 3) How many pieces are B’?
B’ = complement of B = pieces that are NOT black.

From diagram: Only Rook (2) + Neither (14) = 16

✔ Answer: 16

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2) Playing Cards: Clubs (C) and Royal cards (R)

From the Venn diagram:

- Only Clubs (not Royal): 10
- Both Clubs and Royal: 3
- Only Royal (not Clubs): 9
- Outside both (neither): 30

Total cards = 10 + 3 + 9 + 30 = 52 (standard deck — good!)

We need to find:

#### C ∪ R = Clubs OR Royal OR both
= Only Clubs + Only Royal + Both = 10 + 9 + 3 = 22

✔ Answer: 22

#### C’ ∪ R = NOT Clubs OR Royal
C’ = everything outside Clubs = Only Royal (9) + Neither (30) = 39
Then C’ ∪ R = (Not Clubs) OR Royal = Since R is already included in C’, this is just C’ ∪ R = All except Only Clubs.

Alternatively:
C’ ∪ R = (Everything not in C) ∪ R = Everything except the part that is ONLY C.

So: Total - Only Clubs = 52 - 10 = 42

✔ Answer: 42

#### C ∪ R’ = Clubs OR NOT Royal
R’ = everything not Royal = Only Clubs (10) + Neither (30) = 40
C ∪ R’ = Clubs OR Not Royal = Since Clubs includes some Royal, but R’ excludes Royal, so together they cover everything except Only Royal.

So: Total - Only Royal = 52 - 9 = 43

✔ Answer: 43

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## ✔ FINAL ANSWERS SUMMARY:

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Section A

- Even numbers between 1 and 10 = {2, 4, 6, 8, 10}
- Odd numbers between 5 and 15 = {5, 7, 9, 11, 13, 15}

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Section B

- First diagram (Even ∪ Odd): A
- Second diagram (Even ∩ Prime): B
- Third diagram (Even ∩ Square): C

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Section C

#### 1) Chess Board
1) Black and Rooks: 2
2) B ∪ R: All pieces that are black or rooks or both
3) B’: 16

#### 2) Playing Cards
- C ∪ R: 22
- C’ ∪ R: 42
- C ∪ R’: 43

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