can you show working for this problem I need assistance.

1. Derive the Boolean expression for the following circuit diagram. And draw the Truth Table of the resulting circuit diagram. (10 mks] X Y Z F b. Simplify if possible the following Boolean expressions : i. A'C'D + ABCD + AC'D ii. A'B(D' + C'D)' + B(A + A'CD)' iii. X' Z'Y' Z'+Y' Z'+YZ' + X Y [6 marks] c. For the following Boolean expressions: i. A'C'D + ABCD + AC'D' = X ii. A'B(D' + CD) + B(A + A'CD)' = Y Draw the circuit using the basic gates from the original Boolean equations above then simplify these Boolean expressions. [6 marks] d. Using De Morgan's theorem and the Law of Logical equivalence Page 1 of 2 show that: i. (x + y + z)' = X'yz' ii. (xyz)' = x'+ y+z' [6 marks ] e. Prove that : x + yz = (x + y)(x + 2) [ 4 marks ]