(b) Let the universal set $$ \mathcal{U} $$ be the set of real numbers and let $$ A=\{x \in \mathbb{R} $$ : $$ x0\} $$. Find $$ A^{c} $$. (c) Show the intersection of $$ A, B $$ and $$ C $$ in venn diagram.

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(b) Let the universal set $$ \mathcal{U} $$ be the set of real numbers and let $$ A=\{x \in \mathbb{R} $$ : $$ x>0\} $$. Find $$ A^{c} $$. (c) Show the intersection of $$ A, B $$ and $$ C $$ in venn diagram.

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### Part (b)

We are given the universal set $$ \mathcal{U} $$ as the set of real numbers and the set $$ A $$ defined as:

$$
A = \{ x \in \mathbb{R} : x > 0 \}
$$

To find the complement of set $$ A $$, denoted as $$ A^c $$, we need to identify all elements in the universal set $$ \mathcal{U} $$ that are not in $$ A $$.

Since $$ A $$ consists of all positive real numbers, its complement $$ A^c $$ will include:

1. All negative real numbers.
2. The number zero.

Thus, we can express $$ A^c $$ as:

$$
A^c = \{ x \in \mathbb{R} : x \leq 0 \}
$$

### Part (c)

To show the intersection of sets $$ A $$, $$ B $$, and $$ C $$ in a Venn diagram, we need to define the sets $$ B $$ and $$ C $$. However, since the definitions of $$ B $$ and $$ C $$ are not provided, I will describe how to represent the intersection in a Venn diagram.

1. **Draw three overlapping circles**: Each circle represents one of the sets $$ A $$, $$ B $$, and $$ C $$.
2. **Label the circles**: Label them as $$ A $$, $$ B $$, and $$ C $$.
3. **Identify the intersection**: The area where all three circles overlap represents the intersection $$ A \cap B \cap C $$.

If you provide the definitions of sets $$ B $$ and $$ C $$, I can give a more specific representation of the intersection.

Would you like to provide those definitions or need further assistance?
$$ A^c = \{ x \in \mathbb{R} : x \leq 0 \} $$ To show the intersection of sets $$ A $$, $$ B $$, and $$ C $$ in a Venn diagram, draw three overlapping circles labeled $$ A $$, $$ B $$, and $$ C $$. The area where all three circles overlap represents $$ A \cap B \cap C $$.

(b) Let the universal set \( \mathcal{U} \) be the set of real numbers and let \( A=\{x \in \mathbb{R} \) : \( x>0\} \). Find \( A^{c} \). (c) Show the intersection of \( A, B \) and \( C \) in venn diagram.

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