Symbolise the following statements.
There exists at least one number in A={5,7,8,9,10} Which is an even number.

Answer

To symbolize the statement "There exists at least one number in A={5,7,8,9,10} which is an even number," we can follow these steps:

### Step 1: Identify the Set
We have the set \( A = \{5, 7, 8, 9, 10\} \).

### Step 2: Define the Variable
Let \( x \) be a number in the set \( A \).

### Step 3: Define the Property
We need to express that \( x \) is an even number. A number \( x \) is even if there exists an integer \( n \) such that \( x = 2n \).

### Step 4: Formulate the Existence Statement
The statement "There exists at least one number in A which is even" can be symbolized using the existential quantifier \( \exists \). We can write this as:
\[ \exists x \in A \text{ such that } x \text{ is even} \]
In mathematical notation, this can be expressed as:
\[ \exists x \in A, \, (x \text{ is even}) \]

### Step 5: Specify the Even Condition
To specify the condition of being even, we can write:
\[ \exists x \in A, \, (x = 2n \text{ for some integer } n) \]

### Final Symbolized Statement
Thus, the complete symbolized statement is:
\[ \exists x \in A, \, (x = 2n \text{ for some integer } n) \]