6 El-Gharbla Governorate Answer the following questions : 1 Choose the correct answer from the given ones : 1. If $$ \left(2^{x}, \sqrt{y}\right)=(1,1) $$, then $$ x-y= $$ $$ \qquad $$ (a) zero (b) 1 (c) -1 (d) $$ \pm $$ 2. If $$ X=\{1,3\} $$, then $$ n\left(X^{2}\right)= $$ $$ \qquad $$ (a) 2 (b) 4 (c) 3 (d) 10 3) If $$ f(X)=1 $$, then $$ f(1)+f(2)=\ldots \ldots \ldots . . $$.

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Sure, let's tackle each of the questions one by one.

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### **Question 1**
**If $$ \left(2^{x}, \sqrt{y}\right) = (1,1) $$, then $$ x - y = $$ $$ \qquad $$**

**Options:**
- (a) zero
- (b) 1
- (c) -1
- (d) $$ \pm $$

**Solution:**
1. From $$ 2^{x} = 1 $$, we know that $$ x = 0 $$ because $$ 2^0 = 1 $$.
2. From $$ \sqrt{y} = 1 $$, we square both sides to find $$ y = 1 $$.

Now, calculate $$ x - y $$:
$$ x - y = 0 - 1 = -1 $$

**Answer:** **(c) -1**

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### **Question 2**
**If $$ X = \{1,3\} $$, then $$ n\left(X^{2}\right) = $$ $$ \qquad $$**

**Options:**
- (a) 2
- (b) 4
- (c) 3
- (d) 10

**Solution:**
$$ X^{2} $$ represents the Cartesian product $$ X \times X $$. This means all ordered pairs where both elements are from set $$ X $$.

Given $$ X = \{1, 3\} $$:
$$ X^{2} = \{(1,1), (1,3), (3,1), (3,3)\} $$

The number of elements $$ n(X^{2}) $$ is 4.

**Answer:** **(b) 4**

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### **Question 3**
**If $$ f(X) = 1 $$, then $$ f(1) + f(2) = $$ $$ \dots $$**

**Solution:**
Assuming $$ f $$ is a constant function where $$ f(X) = 1 $$ for any input $$ X $$:

$$ f(1) = 1 $$
$$ f(2) = 1 $$

Thus,
$$ f(1) + f(2) = 1 + 1 = 2 $$

**Answer:** **2**

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I hope this clarifies the solutions to your questions!
- **Question 1:** $$ x - y = -1 $$ (Option C) - **Question 2:** $$ n(X^{2}) = 4 $$ (Option B) - **Question 3:** $$ f(1) + f(2) = 2 $$

6
El-Gharbla Governorate

Answer the following questions :
1 Choose the correct answer from the given ones :

If , then
(a) zero
(b) 1
© -1
(d)

If , then
(a) 2
(b) 4
© 3
(d) 10

If , then .

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6 El-Gharbla Governorate Answer the following questions : 1 Choose the correct answer from the given ones : If , then (a) zero (b) 1 © -1 (d) If , then (a) 2 (b) 4 © 3 (d) 10 If , then .