Question

In the following expressions, - represents negation of a variable. For example, -X stands for "NOT x"), + represents logical OR, and juxtaposition represents logical AND (e.g., (x+y)(y+z) represents (X OR y) AND (y OR z). Identify the expression that is satisfiable, from the list below. O a) (-z+x)(-z+-x)(z+x)(z+-x) O b) (-z+-x)(z)(-x+-y)(y+-z) O c) (z+x)(-x+y)(-2)(-y+z) O d) (z)(-z+x)(-z+-x)(x+y)

Answer 1

First of all simplify the expressions. Option -a) (-2+x) (-2+x) CZEX) (2+ X) -> (Z'+x) (Z'+x1) (2 +x) ( 2+x1) Distribution law : AtBC (A+B) CA+C)) 2) (Z'+. Xox!) ( 24 Xox!) negation law : A.A.0) = =)) =) 2) 0 Option-b) (-2+ - x0)(2)(-X +-4) 64 +-2) - (21+x1) (2) (x +4') (4+2) -> (21+X') (x1+ y) (y Z+22') z (21+x! ) C molty!) (42) C: negation Cou) =) (21+x1) (x'y2 + 4'42) o C214x!) ( x142) ( Negation law), =) (2 x'42 + x'x'42)

=) x'x'YZ. Idempotent law A. A A ) = x '42 . ophone : (2+x)(-x+y)(-2)(-4+2) =)(2+x)(x!+4)(2') (y'+z) =) (2 X'dxox'+ x4) (4'2 +22) -) (z x! + xy) (4171) ('negation law). 2) CY'Z'z x+ y' z'xy) 5) Coto) Iingation law) 2) 0 option_d:- (2) (- 2 + x) (-2+ X) (x+4) =) (2) (21+x) (21+x1) (x+4) =) (z) (x+y) ( z17xx) ( Distribuition law) 27 (2) (x +4) CZ') ( .aregation low). 3) 0 (x+4) = 0 Except option-b all are simplified to ocealse). so take option-b as Correct because it is only the satisfiable expression Option -b)