For a Boolean variable 𝑥, which of the following statements is/are FALSE?
2024
For a Boolean variable 𝑥, which of the following statements is/are FALSE?
Answer: B. \(𝑥 + 1 = 𝑥\); C. \(𝑥. 𝑥 = 0\) — Solution: Evaluate each statement for a Boolean variable x: x · 1 = x: True. 1 is the identity for AND, so true AND x equals x. x + 1 = x: False. 1 represents…
- A.
\(𝑥. 1 = 𝑥\) - B.
\(𝑥 + 1 = 𝑥\) - C.
\(𝑥. 𝑥 = 0\) - D.
\(𝑥 + \overline {𝑥} = 1\)
Attempted by 1493 students.
Show answer & explanation
Correct answer: B, C
Solution:
Evaluate each statement for a Boolean variable x:
x · 1 = x: True. 1 is the identity for AND, so true AND x equals x.
x + 1 = x: False. 1 represents logical TRUE, and TRUE OR anything is TRUE, so x + 1 = 1, not x.
x · x = 0: False. By the idempotent law, x AND x equals x, so x · x = x, not 0.
x + not x = 1: True. A variable OR its complement is always TRUE (the complement law).
Therefore, the statements that are FALSE are: x + 1 = x and x · x = 0.
A video solution is available for this question — log in and enroll to watch it.