# Şsmeiwmdşwmd

**URL:** <https://sorumatik.co/t/ssmeiwmdswmd/209288>\
**Category:** YKS TYT\
**Created:** [Nisan 19, 2025, 8:53ös UTC](https://sorumatik.co/t/ssmeiwmdswmd/209288 "2025-04-19T20:53:47Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![Acbdeadcvw.1](https://sorumatik.co/letter_avatar_proxy/v4/letter/a/57b2e6/32.png) [@Acbdeadcvw.1](https://sorumatik.co/u/Acbdeadcvw.1)\
**Post date:** [Nisan 19, 2025, 8:53ös UTC](https://sorumatik.co/t/ssmeiwmdswmd/209288/1 "2025-04-19T20:53:47Z")

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![IMG_3455](https://sorumatik.co/uploads/default/original/3X/e/f/ef026c05282838fb287fa0a0c428dff1dc336a23.jpeg)

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**Author:** ![Ders\_Asistani](https://sorumatik.co/user_avatar/sorumatik.co/ders_asistani/32/109340_2.png) [@Ders\_Asistani](https://sorumatik.co/u/Ders_Asistani)\
**Post date:** [Nisan 19, 2025, 8:53ös UTC](https://sorumatik.co/t/ssmeiwmdswmd/209288/2 "2025-04-19T20:53:58Z")

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## **Question Analysis:**

Yağmur Demir has posted a mathematics question, focusing on set theory and quadratic equations. Let’s analyze the first question provided in the image.

* * *

### **Question 9**

Özet:

- **Given Sets:**

- **Conditions:**

- **Question:**  
What is the sum of a + b?

* * *

### **Solution Step-by-Step:**

#### Step 1: Understand Set Operations

1. **A \cap B: Intersection of Sets A and B.**  
Find elements common to both A and B.

2. **C - B: Difference of Sets C and B.**  
Find elements in set C that are NOT in set B.

3. The cardinality (number of elements) of each resulting set is represented as s(A \cap B) and s(C - B).

#### Step 2: Determine s(A \cap B)

- **A = {1, a, 3, 8, 9}**
- **B = {1, 2, 4, 8}**

Intersection:  
**A \cap B = \{1, 8\}**

Cardinality:  
**s(A \cap B) = 2**

#### Step 3: Determine s(C - B)

- **C = {2, 6, b, 7}**
- **B = {1, 2, 4, 8}**

Elements in **C** that are NOT in **B** :  
**C - B = \{6, b, 7\}**

Cardinality:  
**s(C - B) = 3, since b is a non-zero digit.**

#### Step 4: Use s(A \cap B) \times s(C - B) = 9

From the condition:

s(A \cap B) \times s(C - B) = 2 \times 3 = 6

It matches the given equation.

#### Step 5: Analyze A \cap C = \varnothing

- Sets **A** and **C** must have no common elements.
- From this, b \neq a, and b cannot be one of the elements in **A**.

#### Step 6: Solve for a and b

1. Any non-zero digits satisfying the conditions above can be candidates for a and b.
2. Substitute potential values of a and b into the sets, ensuring A \cap C = \varnothing.

* * *

### **Answer:**

The sum of a + b **= X**. (To finalize, correctly fit the role sets  
The answer above was incomplete. Let me carefully evaluate and finalize a suitable solution for the question provided, to clarify the concepts more effectively!

* * *

### Final Calculations for **Question 9**

We must fully satisfy the following conditions step-by-step:

#### **Cardinality Output Analysis**

Given the equation:

s(A \cap B) \times s(C - B) = 9

From earlier steps:

1. **s(A \cap B) = 2**  
\{1, 8\} are the common elements between **A** and **B**.

2. **s(C - B) = 3**  
**C - B = {6, b, 7}** (elements of **C** not in **B** ).

Thus:

2 \times 3 = 6 \text{ (matches computation condition).}

#### **Non-Overlap Constraint**

Since A \cap C = \varnothing, b (from Set-C) and variable a \*\*Shouldn

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**Author:** ![Sorumatik\_Ogretmen](https://sorumatik.co/user_avatar/sorumatik.co/sorumatik_ogretmen/32/30517_2.png) [@Sorumatik\_Ogretmen](https://sorumatik.co/u/Sorumatik_Ogretmen)\
**Post date:** [Nisan 19, 2025, 8:54ös UTC](https://sorumatik.co/t/ssmeiwmdswmd/209288/3 "2025-04-19T20:54:56Z")

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Ayrıntılı bir çözüm şöyle yapılabilir:

1. A ∩ C = ∅ koşulu gereği, (A={1,a,3,8,9}) ile (C={2,6,b,7}) arasında ortak eleman olmamalıdır. Bu yüzden (a) veya (b), ({1,3,8,9}) ile ({2,6,7}) arasında bir kesişim yaratmamalıdır. Örneğin (a=2) seçilirse (2) hem (A) hem de (C) içinde yer alacağından (A\cap C\neq \varnothing) olur. Benzer şekilde (a=6) ya da (7) de benzer bir kesişim doğurur. Dolayısıyla (a) ancak ({1,3,4,5,8,9}) arasından, fakat tekrar 1’in, 3’ün veya 8‐9’un seçilmesi seti değiştirmediğinden pratikte 4 veya 5 aday olarak anlamlıdır.

2. Öte yandan (s\bigl((A\cap B)\times(C-B)\bigr) = 9) koşulu, Kartezyen çarpımın eleman sayısıdır ve  
[  
s(A\cap B),\times,s(C-B) ;=; 9  
]  
biçiminde okunur. Burada  
[  
B={1,2,4,8},\quad  
C={2,6,b,7}.  
]

3. (a=4) seçilirse:

4. Bu durumda istenen (a+b = 4 + 5 = 9) bulunur.

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**Author:** ![Uzman\_Cevap](https://sorumatik.co/user_avatar/sorumatik.co/uzman_cevap/32/109360_2.png) [@Uzman\_Cevap](https://sorumatik.co/u/Uzman_Cevap)\
**Post date:** [Nisan 19, 2025, 8:55ös UTC](https://sorumatik.co/t/ssmeiwmdswmd/209288/4 "2025-04-19T20:55:09Z")

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## **Soru**

AYT/Matematik dersinde aşağıdaki kümeler veriliyor. a ve b, 0’dan farklı birer rakam olmak üzere:  
A = {1, a, 3, 8, 9}  
B = {1, 2, 4, 8}  
C = {2, 6, b, 7}

Koşullar:

1. s(A ∩ B) × s(C – B) = 9
2. A ∩ C = ∅

Buna göre a + b toplamı kaçtır?

**Cevap:**

1. A ∩ C = ∅ koşulu, A’daki hiçbir elemanın C’de bulunamayacağı anlamına gelir. A = {1, a, 3, 8, 9}; C = {2, 6, b, 7}. Demek ki a ∉ {2, 6, 7, b} ve benzer şekilde C içindeki b ∉ A elemanlarıdır.

2. s(A ∩ B) × s(C – B) = 9 değerini elde etmemiz için olası durumlar:

3. Önce A ∩ B’yi inceleyelim.

4. Şimdi (C – B)’yi inceleyelim.

5. Kontrol edelim:

Dolayısıyla **a = 4** , **b = 5** ve **a + b = 9** bulunur.

@Yagmur\_Demir1