3) Consider the Boolean function f given by the truth table below.PQf(P, Q, R)R11111111111111a) Express f in DNE form. Draw circuit using ^, v, and gates.b) Simplify it if possible and draw this simpler circuit.4) Convert 4,07710 to Binary, Hex and Octal. Then convert Hex back to decimalto verify answers. Must show all your steps for credit.

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Answered: 3) Consider the Boolean function f…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Essentials of DISCRETE MATHEMATICS
show that ( A u B) ˄ ( ^B u C) -> ( A v C ) is a tautology
EX LeT X = {!,2,3,415,6} T-{x,,てり,E4),し) 「ス45 Topology.?
Solve for the general solution of the equation: 2x’’+ 200x = 0. Show all math steps.
Exercise 2 Given KB = (X→Y) ^ (Y→Z), and a = (X→Z) Is KB |= a is valid or not?
If p= You can pass the Discrete Structures exam, q= you are regular in class and r = you are studying at home , then translate the following English sentence into a logical expression. "You can pass the Discrete Structures exam only if you are regular in class or you are studying at home." O (qV r) → p O (q ^ p) → r O (r ^p) → q O (q^ r) → p none of the choices
1. Check whether it includes Tautology, Contradiction or Contingency.based on the table in image (Please answer max 60 minutes answer u now, and reject thank u. This is problem about math Logical mathrmatical)
How can I solve this problem?
Match the logical equivalence on the left with its name on the right. i Instructions P^T = P pv T = T pvp = p -(¯)=p pv (p^q) = p |||
2. Write negations of the following conditional statements: - (p→q) = p^~q (a) VneZ,ifn divisible by 2 then n is divisible by 2. (b) VxeR, if x(x+1)> 0 then x >0 or x<-1

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3) Consider the Boolean function f given by the truth table below. PQR 0 0 0 0 0 0 1 0 1 f(P, Q, R) 1 1 1 1 1 1 1 1 1 1 1 1 a) Express f in DNF form. Draw circuit using ^, v, and " gates. b) Simplify it if possible and draw this simpler circuit.