Draw Venn diagram to represent the truth of the statement "No child is naughty"
Where U = Universal set of human beings
C = Set of children
N = Set of naughty persons

Options

A.
B.
C.
D. None of these

Answer

To represent the statement "No child is naughty" using a Venn diagram, we will follow these steps:

### Step 1: Define the Universal Set
We start by defining the universal set \( U \), which represents all human beings. We will draw a rectangle to represent this universal set.

**Hint:** Remember that the universal set contains all possible elements relevant to the discussion.

### Step 2: Draw the Set of Children
Next, we will draw a circle inside the rectangle to represent the set of children, denoted as \( C \). This circle will contain all the elements that are children.

**Hint:** The circle represents a specific subset of the universal set.

### Step 3: Draw the Set of Naughty Persons
Now, we will draw another circle to represent the set of naughty persons, denoted as \( N \). However, since the statement says "No child is naughty," this circle will not overlap with the circle representing children.

**Hint:** The lack of overlap indicates that there are no elements that belong to both sets.

### Step 4: Ensure No Intersection
To illustrate the statement "No child is naughty," we ensure that the circles \( C \) and \( N \) do not intersect at all. This means that the area representing children does not touch the area representing naughty persons.

**Hint:** The absence of intersection signifies that there are no common elements between the two sets.

### Step 5: Label the Diagram
Finally, we label the rectangle as \( U \) for the universal set, the circle for children as \( C \), and the circle for naughty persons as \( N \).

**Hint:** Proper labeling helps in understanding the representation clearly.

### Final Venn Diagram
The final Venn diagram will consist of:
- A rectangle labeled \( U \) representing all human beings.
- A circle inside the rectangle labeled \( C \) representing children.
- A separate circle labeled \( N \) representing naughty persons, which does not intersect with circle \( C \).

This Venn diagram effectively represents the truth of the statement "No child is naughty."