$$X Y Z+X Y' Z'+X' Y' Z+X' Y Z'$$
I know it simplify to (X XOR Y XOR Z),BUT I want to simplified using only AND, OR, and NOT Gates?
Please help I spent three hours but I don't get the same truth table.
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1If you want a sum of products, then $X Y Z+X Y' Z'+X' Y' Z+X' Y Z'$ is as simplified as you can get it. – Adriano Oct 04 '14 at 00:08
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Thank you I though am going crazy. – Abdalla Oct 04 '14 at 00:29
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I suppose the prime means negation and then $X'=1+X$ etc.
$XYZ+XY'Z'+X'Y'Z+X'YZ'=$ $XYZ+X(1+Y)(1+Z)+(1+X)(1+Y)Z+(1+X)Y(1+Z)=$ $XYZ+X(1+Y+Z+YZ)+(1+X+Y+XY)Z+(Y+XY)(1+Z)=$ $XYZ+X+XY+XZ+XYZ+Z+XZ+YZ+XYZ+Y+YZ+XY+XYZ=$ $X+Y+Z$
Since $X+Y=(X\vee Y)\wedge \neg(X\wedge Y)$ just use AND, OR and NOT to construct $X+Y+Z$, that is $X$ XOR ($Y$ XOR $Z$)
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Let T : C3 → C3 be the linear operator defined by T(z1, z2, z3) = (z1 + iz2, iz2 - z3, z1 + z3). (1.1) Find a formula for T ∗(z1, z2, z3) expressed as a single vector in terms of z1, z2, z3. (1.2) Find a basis for N (T) . (1.3) Find a basis for R (T ∗) . (1.4) Show that R (T ∗)⊥ = N (T) .
