1. (a) Prove by algebraic method that ¯a + ab + ac¯+ a ¯bc¯ = ¯a + ¯b + ¯c.
(b) Find the CPOS of f(x, y, z) = (x + ¯y)y + ¯xz + x + y + ¯y(x + z).
Prove by algebraic method 1. (a) (10pts) Prove by algebraic method that a+ ab + ač + abe-a++. + zz + x + u+5(FT ). (b) (10pts) Find the CPOS of f(x, y, z)-(x +
Prove by algebraic method that a ̄ + ab + ac ̄ + a ̄bc ̄ = a ̄ + ̄b + c ̄.
2.7 Exercises 43 4. Prove each of the following identities by using the algebraic rules (no truth tables). Several steps may be combined, but make sure that each step is clear (a) a'b b'c + a'c (b) а'd + ac (c) xz' + x'y' + x'z + y'z = y' + x'z + xz' (d) ad' a'b' + c'd + a'c' + b'd = ad' + (bc' (e) xy' z(x' + y + w) (f) a'z' yz + xy' =...
Prove the following using appropriate methods. 10) a AC + AB + BC = AB + BC + AC b. AC + BC + AB EBC + AB+ AC
Points W and X are chosen on the side AB of triangle ABC and points Y and Z are chosen on side AC. Suppose that cr(A,W,X,B)=cr(A,Y,Z,C) and that WY is parallel to XZ. Prove that XZ is parallel to BC. Hint: let T be the point where the parallel to XZ through B meets line AC. Note that neither a nor Y can lie on segment TC and use excercise 3C.2 to show that T is C. cr=cross ratio
1) Implement the following equations using PLA: X=AB'D+A\c+BC+CD! Y=A\c'+AC+CD Z=CD+A/C +AB/D
R= ABCDEG decomposition: {AB, BC, ABDE, EG } F = {AB → C, AC → B, AD → E, B → D, BC → A, E → G} Is this lossless or not? Please Draw a table for this, the answer set online told me this is lossy, but when I do the table test, I find it is lossless.
Using congruence axiom 1 prove that If A-B-C then ABAC, AB>AC or AC>AB
8. (2 points) Consider the mechanism below Step 1 (slow) A2 BC AB+AC AB BC B2AC Step 2 (fast) B2+ 2 AC overall A22 BC What is the rate law of the reaction? a. b. What compound is considered an intermediate?
5. Prove each of the following set equalities both by Venn Diagram and by algebraic method. (a) A - (B C) = (A - B) (A - C) (b) A - (B C) = (A - B) (A - C) (c) A (B - C) = (A B) - C = (A B) - (A C) Hint: To prove the last form, use the equality A C' = A (A' C'). (d) A (B - C) = (A B) (A...