Multiple choice

Which of the following Boolean expressions is always true?

  1. 10 <= x && !(x >= 10)

  2. y = = x + y && x = = x + y

  3. 10 <= x | | !( x >= 10)

  4. y = = x + y | | x = = x + y
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Option C is always true by the law of excluded middle: either x >= 10 or x < 10 must hold. The expression 10 <= x || !(x >= 10) simplifies to (x >= 10) || !(x >= 10), which is a tautology. Option A is always false (contradiction). Options B and D are not tautologies - they assert specific arithmetic relationships between variables that may not hold.

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