State whether each of the following statements is true or false :
Every integer is either positive or negative.

Answer

To determine whether the statement "Every integer is either positive or negative" is true or false, we can analyze the definition of integers.

### Step 1: Understand the definition of integers
Integers include all whole numbers, both positive and negative, as well as zero. This means that the set of integers can be represented as:
- Positive integers: 1, 2, 3, ...
- Negative integers: -1, -2, -3, ...
- Zero: 0

### Step 2: Analyze the statement
The statement claims that every integer is either positive or negative. However, we have identified that zero is also an integer. Since zero is neither positive nor negative, this contradicts the statement.

### Step 3: Conclusion
Since there exists at least one integer (which is zero) that is neither positive nor negative, the statement "Every integer is either positive or negative" is false.

### Final Answer
The statement is **false**.

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