Check the validity of the following statement " Square of an integer is positive or negative " .

Answer

To check the validity of the statement "Square of an integer is positive or negative", we will analyze the components of the statement step by step.

### Step 1: Understand the statement
The statement is a compound statement that consists of two parts:
1. The square of an integer is positive.
2. The square of an integer is negative.

### Step 2: Analyze the first component
Let's evaluate the first part: "The square of an integer is positive."
- An integer can be positive, negative, or zero.
- When we square any integer (positive, negative, or zero), the result is always non-negative.
- For example:
- \( 2^2 = 4 \) (positive)
- \( (-2)^2 = 4 \) (positive)
- \( 0^2 = 0 \) (non-negative)
- Therefore, the first statement is **true** since the square of any integer is always non-negative.

### Step 3: Analyze the second component
Now, let's evaluate the second part: "The square of an integer is negative."
- A square of an integer cannot be negative.
- Since squaring any integer results in a non-negative value (as shown above), this statement is **false**.

### Step 4: Evaluate the compound statement
The original statement uses "or," which means that for the compound statement to be valid, at least one of the component statements must be true.
- We found that the first statement is true, and the second statement is false.
- Since at least one statement (the first one) is true, the compound statement "Square of an integer is positive or negative" is **valid**.

### Conclusion
Thus, we conclude that the statement "Square of an integer is positive or negative" is valid because one of its components is true.

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