Apply De-Morgan’s theorem to the following expressions. (a)  ((A+BC’)’+D(E+F’)’)’   (b)  ((A+B+C)D)’ (c)  (ABC+DEF)’ (d)  (AB’+CD’+EF)’

Simplify the following expressions by applying Boolean rules. EF'G + EF' + G

) Translate the following argument into the language of PL and show it is valid by giving a derivation.   Every planet except Earth is LIFELESS1. Therefore, given any distinct two planets, at least one of them is lifeless. (UD: Planets)

Data Mining - cosine similarity, Jaccard coefficient, Euclidean distance, correlation coefficient.

If w is TRUE, x is TRUE, and y is FALSE, what is ((w AND x AND y') OR (w' AND x AND y')) AND ((w AND x AND y') AND (w' AND x AND y'))'?

Simplify these  two given Boolean expressions1. AB+AB’2. (A+B)(A+B’)

(1) (a) Let r, 1, and r, be regular expression. Find all the regular ones from the following expression s: 2, r'-0. ((r')). r), n -n +½. (b) Given a regular expression 7; = a(ab)* +b°a*, r, = (b + a)* +a*, find L(;) and L(r,), the languages associated with i and r3, respective ly. (c) Find a regular expression r such that L(r) is the same as L = {b"ab",(ba)* : n, m2 0,h2 1}. %3D

Simplify the following expressions by applying Boolean rules. A + B' + C' . C + A' + B

3. Construct the DAG for the expression: ((a+b) - (a - b)) * (a − b) +((a+b) — (a - b))

Using the following variable bindings: (setq x ‘(a b c d)) (setq y ‘(1 2 3 4)) Using only variables x and y, car, cdr, and cons, use Lisp expressions to generate: