A Level Computer Science OCR Test 2025 – 400 Free Practice Questions to Pass the Exam

To understand why the simplified result of the expression X v (XY) is X, we can analyze the expression using Boolean algebra.

The expression consists of two parts: X and XY, where v denotes the logical OR operation. According to the laws of Boolean algebra, specifically the absorption law, we can simplify expressions that include a variable and its conjunction with another expression.

The absorption law states that for any boolean variable X and any expression Y, the following holds true:

- X v (X ∧ Y) = X

In your expression, XY can be considered as Y when dealing with the absorption law since X is already included in the OR operation. Hence, when you have X v (XY), it means if either X is true or XY is true, the overall expression will evaluate to true. However, if X is true, the truth value of XY becomes irrelevant because the result will still be true due to the presence of X.

Therefore, regardless of the value of Y, as long as X is true, the entire expression evaluates to true. When X is false, the part XY also becomes false provided Y is not true or X must be true for the output to be true. Thus the overall simplified result effectively returns