Question-197040

Question Number 197040 by peter frank last updated on 06/Sep/23

Commented by TheHoneyCat last updated on 08/Sep/23

a)

Q = X Y + \bar{X Z} + Y Z

= (X + \bar{X}) (X Y + \bar{X Z} + Y Z)

= (X Y + X Y Z) + (\bar{X Z} + \bar{X Y Z})

= (X (Y + Y Z)) + (\bar{X} (Z + Y Z))

= (X Y) + (\bar{X Z})

= X Y + \bar{X Z}

OR [AND [X, Y], AND [NOT [X], Z]]

Commented by TheHoneyCat last updated on 08/Sep/23

b)

Q = X Y + X Z + Y (Y + Z) + X Y

= X Y + X Z + Y (Y + Z)

= X Y + X Z + Y Y + Y Z

= X Y + X Z + Y + Y Z

= X Y + X Z + Y

= X Z + Y

OR [Y, AND [X, Z]]

Commented by TheHoneyCat last updated on 08/Sep/23

c)

let W := X + Y

Q = W (W + Z)

= W + W Z

= W

= X + Y

OR [X, Y]

Commented by TheHoneyCat last updated on 08/Sep/23

d)

let W := X Y

Q = W + W Z + W \bar{Z}

= W

= X Y

AND [X, Y]

Commented by peter frank last updated on 10/Sep/23

thank you

Commented by TheHoneyCat last updated on 11/Sep/23

you're welcome

Answered by TheHoneyCat last updated on 08/Sep/23

e)

Q = X \bar{Y}

AND [X, NOT [Y]]