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

Question

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))

Accepted Answer

(B). Option (B) is correct because the function X produces a '1' when at least two inputs are '1'. In this case, if a and b are both '1', adding another '1' (from c) does not change the output, confirming that X(a,b,X(a,b,c)) equals X(a,b,c).

Solution

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