Given, universal set =`{x in Z: -6 lt x le 6}`, N={n:n is a non-negative number} and P={x:x ia a non-positive number}. Find:
(i) N', (ii) P'

Answer

To solve the problem, we need to find the complements of the sets N and P with respect to the universal set U.

### Step 1: Define the Universal Set U
The universal set is defined as:
\[ U = \{ x \in \mathbb{Z} : -6 < x \leq 6 \} \]
This means U includes all integers from -5 to 6. Therefore, we can list the elements of U:
\[ U = \{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6\} \]

### Step 2: Define the Set N
Set N is defined as:
\[ N = \{ n : n \text{ is a non-negative number} \} \]
In the context of the universal set, the non-negative integers from U are:
\[ N = \{0, 1, 2, 3, 4, 5, 6\} \]

### Step 3: Find the Complement of Set N (N')
The complement of set N, denoted as N', is defined as:
\[ N' = U - N \]
This means we will take all elements from U and remove those that are in N:
\[ N' = \{-5, -4, -3, -2, -1\} \]

### Step 4: Define the Set P
Set P is defined as:
\[ P = \{ x : x \text{ is a non-positive number} \} \]
In the context of the universal set, the non-positive integers from U are:
\[ P = \{0, -1, -2, -3, -4, -5\} \]

### Step 5: Find the Complement of Set P (P')
The complement of set P, denoted as P', is defined as:
\[ P' = U - P \]
This means we will take all elements from U and remove those that are in P:
\[ P' = \{1, 2, 3, 4, 5, 6\} \]

### Final Answers
(i) \( N' = \{-5, -4, -3, -2, -1\} \)
(ii) \( P' = \{1, 2, 3, 4, 5, 6\} \)

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