Question

4. Proof and simplification (16 points) a) Show that the following equation is valid using Boolean algebra axioms and theorems. Demonstrate your detailed steps. (8 points) BC+Ā B+AC = ABC+Ā b) Simplify the following logic equation: (8 points) F(X,Y,Z)=Y Z + XY + XZ + YZ

I just need help with the second one

Answer 1

Answerb - Given Logic equation - F(x, y, z) Ý Ž + x Ý + x 2 + y z = Ý Ž + y + xÝ + X z [ Rearranging the terms E X į (Y+Y) + x 9 + X 2 [Taking & a remor] = .1 + xy + x2 [+y=1 = ž:(1+x) + x Ý +X 2 [By identity : = ².1 + x + x Ý + x 2 [open the bracker] - 2 ZÝ 4 ºz + x 7 [Rev. ] = ( ž) Ž + x ² + 2) + x 7 [Taking & as Ž +8.1 + x [2+2 = 1 Ž + X (1+%) [Taking Ž + X 1 [1+9 = 1 By Identity Property IF(x,y,z) the common X х Common - Z + x

Ý Ž X Y Zyz yz + xy + x2 + y2 xtz To verify the through above Logic equation Truth Table - with simplified equat х Y Z N Ž T (Given Ean). (simplific 1 1 0 1 0 1 1 0 O 1 1 O 0 1 1 0 O 1 1 0 0 1 1 - O - OOO Оооо 0 0 O - O 0 1 O o O