The simplified form of the Boolean expression $Y = (¯ A B C + D) (¯ A D + ¯ B ¯ C)$ can be written as

A D + B C D

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A D + B C D

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A D + B C D

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(A + D) (B C + D)

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Solution

The correct option is B $A D + B C D$
$Y = (A B C + D) (A D + B C) = A B C D + A D + B C D = (A D + B C D) (B C + 1 = 1)$

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The boolean expression X Y Z + X Y Z + XY Z + X Y Z + XYZ can be simplified to

¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ (a + ¯ b + c + ¯ d) + (b + ¯ c)

(¯ A ¯ B ¯ C + ¯ A B ¯ C + ¯ A B C + A B ¯ C)

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