(c) Write $$ \{x \in U \mid x=2 n+1 $$ for some $$ n \in N\} $$ by listing the elements in braces. Choose the correct answer below. A. $$ \varnothing $$ B. $$ \{3,5,7,9,11,13,15,17,19\} $$ C. $$ \{1,2,3,4,5,6,7,8,9\} $$ D. $$ \{2,4,6,8,10,12,14,16,18,20\} $$

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To solve the problem, we need to interpret the set notation given:

$$
\{x \in U \mid x=2n+1 \text{ for some } n \in N\}
$$

Here, $$ U $$ is the universal set, and $$ N $$ typically represents the set of natural numbers, which usually starts from 1 (i.e., $$ N = \{1, 2, 3, \ldots\} $$).

The expression $$ x = 2n + 1 $$ describes all odd numbers that can be generated by substituting natural numbers $$ n $$ into the equation.

Let's calculate the first few values of $$ x $$ for $$ n = 1, 2, 3, \ldots $$:

- For $$ n = 1 $$: $$ x = 2(1) + 1 = 3 $$
- For $$ n = 2 $$: $$ x = 2(2) + 1 = 5 $$
- For $$ n = 3 $$: $$ x = 2(3) + 1 = 7 $$
- For $$ n = 4 $$: $$ x = 2(4) + 1 = 9 $$
- For $$ n = 5 $$: $$ x = 2(5) + 1 = 11 $$
- For $$ n = 6 $$: $$ x = 2(6) + 1 = 13 $$
- For $$ n = 7 $$: $$ x = 2(7) + 1 = 15 $$
- For $$ n = 8 $$: $$ x = 2(8) + 1 = 17 $$
- For $$ n = 9 $$: $$ x = 2(9) + 1 = 19 $$

Thus, the set of elements generated by this expression is:

$$
\{3, 5, 7, 9, 11, 13, 15, 17, 19\}
$$

Now, let's compare this with the provided options:

A. $$ \varnothing $$  
B. $$ \{3,5,7,9,11,13,15,17,19\} $$  
C. $$ \{1,2,3,4,5,6,7,8,9\} $$  
D. $$ \{2,4,6,8,10,12,14,16,18,20\} $$

The correct answer is:

**B. $$ \{3,5,7,9,11,13,15,17,19\} $$**
The correct answer is $$ \{3,5,7,9,11,13,15,17,19\} $$, choice B.

© Write for some by listing the elements in braces. Choose the correct answer below.
A.
B.
C.
D.

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