. Let F(X, Y, Z)=(X + Y + Z)(X + Y + Z)(X + Y + Z)(X + Y + Z). Use a 3-variable K-Map to find the minimized SOP form of this function. Hint: When you go to fill in the K-Map, you may have trouble figuring out where to put the 0s and 1s because F is specified in POS form. Your first impulse may be to try to multiply out these terms to convert it into SOP form, and then use that to fill in the K-Map. This would be logically correct but a ton of work. Instead you can use the POS form to determine where to place the 0s in the K-Map. For example, the first term (X+Y +Z) implies that you should put a zero in the square that corresponds to (X + Y + Z¯). Now use DeMorgan’s to see that (X + Y + Z¯) = X ·Y ·Z and place a 0 in the corresponding square. Repeat this for all the product terms; then you can fill in 1s in the squares without 0s.

Write a function balancechemical to balance chemical reactions by solving a linear set of equations. the inputs arguments are: reagents: symbols of reagents in string row array products: symbols of products in string row array elements: elements in the reaction in string row array elcmpreag: elemental composition of reactants in two dimensional numeric array elcmpprdcts: elemental composition of prducts in two dimensional numeric array hint: the first part of the problem is setting up the set of linear equations that should be solve. the second part of the problem is to find the integers from the solution. one way to do this is to mulitiply the rational basis for the nullspace by increasing larger integers until both the left-and right-side integers exist. for example, for the reaction that involves reacting with to produce and : reagents=["ch4", "o2"]; products =["co2", "h2o"]; elements =["c","h", "o"] elcmpreag=[1,4,0;

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