Question

Write 10 junior high mathematics quizzing competition questions with their respective answers using step by step method on the topic domian of two sets

Answer 1

Sure! Below are 10 junior high mathematics quiz questions related to the domain of two sets, along with step-by-step solutions for each question.

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### Question 1
**If Set A = {1, 2, 3} and Set B = {2, 3, 4}, what is the domain of A and B?**

#### Answer:
1. **Identify Set A and Set B**:
A = {1, 2, 3}
B = {2, 3, 4}

2. **Combine Elements from Both Sets**:
Domain = {x | x ∈ A or x ∈ B}
= {1, 2, 3, 4}

**Domain of A and B = {1, 2, 3, 4}**

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### Question 2
**Let Set C = {5, 6, 7} and Set D = {6, 7, 8, 9}. What is the union of C and D?**

#### Answer:
1. **Identify Set C and Set D**:
C = {5, 6, 7}
D = {6, 7, 8, 9}

2. **Find Union of Sets (Combine without Duplicates)**:
C ∪ D = {5, 6, 7, 8, 9}

**Union of C and D = {5, 6, 7, 8, 9}**

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### Question 3
**Given Set E = {a, b} and Set F = {b, c, d}, what is the intersection of E and F?**

#### Answer:
1. **Identify Set E and Set F**:
E = {a, b}
F = {b, c, d}

2. **Find Intersection of Sets (Common Elements)**:
E ∩ F = {b}

**Intersection of E and F = {b}**

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### Question 4
**If Set G = {2, 4, 6, 8} and Set H = {1, 2, 3, 4}, what is the difference G - H?**

#### Answer:
1. **Identify Set G and Set H**:
G = {2, 4, 6, 8}
H = {1, 2, 3, 4}

2. **Find Elements in G that are not in H**:
G - H = {6, 8}

**Difference G - H = {6, 8}**

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### Question 5
**Consider Set I = { x ∈ ℕ | x < 5 } and Set J = { x ∈ ℕ | x > 2 }. What is the domain of I and J?**

#### Answer:
1. **Identify the Natural Numbers in Set I and Set J**:
I = {1, 2, 3, 4}
J = {3, 4, 5, ...}

2. **Combine Elements from Both Sets**:
Domain = {x | x ∈ I or x ∈ J}
= {1, 2, 3, 4, 5, ...}

**Domain of I and J = {1, 2, 3, 4, 5, ...}**

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### Question 6
**Let Set K = {x | x is an even number less than 10} and Set L = {x | x is a prime number less than 10}. What is the intersection of K and L?**

#### Answer:
1. **Identify Set K and Set L**:
K = {0, 2, 4, 6, 8}
L = {2, 3, 5, 7}

2. **Find Intersection of Sets**:
K ∩ L = {2}

**Intersection of K and L = {2}**

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### Question 7
**If Set M = {1, 3, 5, 7} and Set N = {5, 6, 7, 8}, find the symmetric difference of M and N.**

#### Answer:
1. **Identify Set M and Set N**:
M = {1, 3, 5, 7}
N = {5, 6, 7, 8}

2. **Compute M - N and N - M**:
M - N = {1, 3}
N - M = {6, 8}

3. **Combine Results**:
Symmetric Difference = (M - N) ∪ (N - M) = {1, 3} ∪ {6, 8} = {1, 3, 6, 8}

**Symmetric Difference of M and N = {1, 3, 6, 8}**

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### Question 8
**Let Set O = {10, 20, 30} and Set P = {20, 40}. What is the Cartesian product O x P?**

#### Answer:
1. **Identify Set O and Set P**:
O = {10, 20, 30}
P = {20, 40}

2. **Form Pairs (Cartesian Product)**:
O x P = {(10, 20), (10, 40), (20, 20), (20, 40), (30, 20), (30, 40)}

**Cartesian Product O x P = {(10, 20), (10, 40), (20, 20), (20, 40), (30, 20), (30, 40)}**

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### Question 9
**If Set Q = {x | x is an integer, -3 ≤ x ≤ 3} and Set R = {x | x is a positive integer ≤ 3}, determine the domain of Q and R.**

#### Answer:
1. **List elements of Set Q and Set R**:
Q = {-3, -2, -1, 0, 1, 2, 3}
R = {1, 2, 3}

2. **Combine Elements**:
Domain = {-3, -2, -1, 0, 1, 2, 3}

**Domain of Q and R = {-3, -2, -1, 0, 1, 2, 3}**

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### Question 10
**Let Set S = {3, 6, 9} and Set T = {9, 12, 15}. Find the union and then the intersection of S and T.**

#### Answer:
1. **Identify Set S and Set T**:
S = {3, 6, 9}
T = {9, 12, 15}

2. **Find Union**:
S ∪ T = {3, 6, 9, 12, 15}

3. **Find Intersection**:
S ∩ T = {9}

**Union of S and T = {3, 6, 9, 12, 15}, Intersection = {9}**

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Feel free to use these questions and answers in your mathematics quiz competition!