question 1 please 1. Convex Programming Prove that the following mathematical program is a convex program. Youmay use without proof any facts claimed about convex functions and sets in the lecture slides.min max(1/₁, 1/₂)1,2F1, F₂ > 0x² + x² ≤ 12. Propositional Inference Suppose you want to show:A^B^ (B⇒D) ^ ((A^D) E) ^ ((BAC) ⇒F) ^ (A⇒C) ^ (F⇒G) G(a) Draw the diagram we used in the video for forward and backward chaining.(b) Indicate the order in which symbols are popped from the agenda by forward chaining(c) Indicate the order in which subgoals are added to the stack by backwards chaining(d) Prove the entailment using resolution. (You do not need to show every clause generated, justthose on the path to G.(e) Draw the tree of models explored by DPLL to prove the entailment.3. Limits of Forward ChainingGiven an example of an entailment that can be inferred via resolution but cannot be inferred usingforward chaining

1. Convex Programming Prove that the following mathematical program is a convex program. You may use without proof any facts claimed about convex functions and sets in the lecture slides. min max(1/11, 1/12) #1-72 71, 7₂0 x² + x² ≤1

1. Convex Programming Prove that the following mathematical program is a convex program. You may use without proof any facts claimed about convex functions and sets in the lecture slides. min max(1/11, 1/12) #1-72 71, 7₂0 x² + x² ≤1

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

question 1 please

1. Convex Programming Prove that the following mathematical program is a convex program. You
may use without proof any facts claimed about convex functions and sets in the lecture slides.
min max(1/₁, 1/₂)
1,2
F1, F₂ > 0
x² + x² ≤ 1
2. Propositional Inference Suppose you want to show:
A^B^ (B⇒D) ^ ((A^D) E) ^ ((BAC) ⇒F) ^ (A⇒C) ^ (F⇒G) G
(a) Draw the diagram we used in the video for forward and backward chaining.
(b) Indicate the order in which symbols are popped from the agenda by forward chaining
(c) Indicate the order in which subgoals are added to the stack by backwards chaining
(d) Prove the entailment using resolution. (You do not need to show every clause generated, just
those on the path to G.
(e) Draw the tree of models explored by DPLL to prove the entailment.
3. Limits of Forward Chaining
Given an example of an entailment that can be inferred via resolution but cannot be inferred using
forward chaining

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