Given the function F (X, Y , Z)=Σm(0,1, 2 , 4 , 6)

answer the following questions:

1. Obtain the expression in the Canonical Disjunctive Normal Form

2. Obtain the expression in the Canonical Conjunctive Normal Form

3. Derive the truth table for both the Minterms and Maxterms

4. Obtain the minimized SOP and POS

5. Draw the resultant circuit diagram for the minimized SOP

Prove the converse of the pythagorean theorem using similar triangles. the converse of the pythagorean theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squares length of the hypotenuse, the triangle is a right triangle. be sure to create and name the appropriate geometric figures.

Ahmed plans to add a rectangular sunroom to his house. the sunroom will have a length of 14 feet and a width of 10 feet, and the construction will cost $40 per square foot. how much more would the sunroom cost if it’s width were increased to 12 feet?

Anew obstacle course is home to several new types of challenging obstacles. one such obstacle is traversing a 15-stair staircase. to make it more challenging, the stairs are not uniformly spaced. rather, the vertical space between consecutive stairs for the first 10 stairs is 113 feet and the vertical space for the last 5 stairs is 134 feet. what is the total vertical distance traveled ascending and descending the entire 15-stair staircase?