If `x` is a rational number and `y` is an irrational number, then both `x\ +\ y\ a n d\ x y` are necessarily rational both `x\ +\ y\ a n d\ x y` are necessarily irrational `x y` is necessarily irrational, but `x\ +\ y` can be either rational or irrational `x\ +\ y` is necessarily irrational, but `x y` can be either rational or irrational

Explanation

To solve the question, we need to analyze the properties of rational and irrational numbers when they are added or multiplied.

### Step-by-Step Solution:

1. **Define Rational and Irrational Numbers**:
- A rational number is any number that can be expressed as the quotient of two integers (e.g., \( \frac{a}{b} \) where \( b \neq 0 \)).
- An irrational number cannot be expressed as a simple fraction; it has a non-repeating, non-terminating decimal expansion (e.g., \( \sqrt{2}, \pi \)).

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