Question

For a Boolean variable \(x\), which of the following statements is/are FALSE?}

• A. \(x \cdot 1 = x\)
• B. \(x + 1 = x\)
• C. \(x \cdot x = 0\)
• D. \(x + \overline{x} = 1\)

Hint:

Boolean algebra follows basic logic rules: \(x + 1 = 1\), \(x \cdot x = x\), and \(x + \overline{x} = 1\). Review these rules for accuracy.

Answer 1

The Correct Option is B

Option (A): This is true. The Boolean AND operation with 1 always yields the variable itself: \(x \cdot 1 = x\).
Option (B): This is false. The Boolean OR operation with 1 always yields 1, regardless of the value of \(x\): \(x + 1 = 1\).
Option (C): This is false. The Boolean AND operation with itself yields the variable itself: \(x \cdot x = x\), not 0.
Option (D): This is true. The Boolean OR operation with the complement of a variable always yields 1: \(x + \overline{x} = 1\). Final Answer: \[ \boxed{\text{(B), (C)}} \]