Let \(𝑋\) be a 3-variable Boolean function that produces output as ‘1’ when…

GATE · 2025 · CS · Set 1 · Computer Science & IT

Let $𝑋$ be a 3-variable Boolean function that produces output as ‘1’ when at least two of the input variables are ‘1’. Which of the following statement(s) is/are CORRECT, where $𝑎, 𝑏, 𝑐, 𝑑,𝑒$ are Boolean variables?

A.
$𝑋(𝑎, 𝑏, 𝑋(𝑐, 𝑑,𝑒)) = 𝑋(𝑋(𝑎, 𝑏, 𝑐), 𝑑,𝑒)$
B.
$𝑋(𝑎, 𝑏, 𝑋(𝑎, 𝑏, 𝑐)) = 𝑋(𝑎, 𝑏, 𝑐)$
C.
$𝑋(𝑎, 𝑏, 𝑋(𝑎, 𝑐, 𝑑)) = (𝑋(𝑎, 𝑏, 𝑎) AND 𝑋(𝑐, 𝑑, 𝑐))$
D.
$𝑋(𝑎, 𝑏, 𝑐) = 𝑋(𝑎, 𝑋(𝑎, 𝑏, 𝑐), 𝑋(𝑎, 𝑐, 𝑐))$

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