Write each of the following sets in Roster form and write the cardinal number of each .
E = ` {x: x =2n- 1 , n in N and n lt 6.}`

Answer

To solve the problem, we need to express the set E in roster form and find its cardinal number. Let's go through the steps systematically.

### Step 1: Identify the values of n
We are given that \( n \) is a natural number and \( n < 6 \). The natural numbers less than 6 are:
\[ n = 1, 2, 3, 4, 5 \]

### Step 2: Substitute values of n into the expression
The expression for \( x \) is given as:
\[ x = 2n - 1 \]
We will substitute each value of \( n \) into this expression:

1. For \( n = 1 \):
\[ x = 2(1) - 1 = 2 - 1 = 1 \]

2. For \( n = 2 \):
\[ x = 2(2) - 1 = 4 - 1 = 3 \]

3. For \( n = 3 \):
\[ x = 2(3) - 1 = 6 - 1 = 5 \]

4. For \( n = 4 \):
\[ x = 2(4) - 1 = 8 - 1 = 7 \]

5. For \( n = 5 \):
\[ x = 2(5) - 1 = 10 - 1 = 9 \]

### Step 3: Write the set in roster form
Now, we can compile the results from the substitutions into a set:
\[ E = \{1, 3, 5, 7, 9\} \]

### Step 4: Determine the cardinal number
The cardinal number of a set is the number of elements in that set. In this case, the set \( E \) has 5 elements:
\[ \text{Cardinal number of } E = 5 \]

### Final Answer
Thus, the set in roster form is:
\[ E = \{1, 3, 5, 7, 9\} \]
And the cardinal number of the set \( E \) is:
\[ 5 \]

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