A Level Computer Science OCR Practice Exam

What is the simplified result of the expression Xv(XY)?

1. X

2. XY

3. X ∧ Y

4. X ∨ Y

The correct answer is: X

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