Which of the following Semigroup instances are lawful?   Please show the solution for each option.

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
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Which of the following Semigroup instances are lawful?

 

Please show the solution for each option.

Monoids and Semigroups
Question 5
Which of the following Semigroup instances are lawful?
1. О
newtype X = X Int
instance Semigroup X where
Ха <> Х ь 3D х (а + b)
2. O
newtype X = X Int
instance Semigroup X where
Ха <> X ь 3D х (а — b)
3.
newtype X = X Int
instance Semigroup X where
Ха <> Х ь - х (аbs (a + b))
4. O
newtype X = X Int
instance Semigroup X where
Ха <> X ь %3D Ха
Transcribed Image Text:Monoids and Semigroups Question 5 Which of the following Semigroup instances are lawful? 1. О newtype X = X Int instance Semigroup X where Ха <> Х ь 3D х (а + b) 2. O newtype X = X Int instance Semigroup X where Ха <> X ь 3D х (а — b) 3. newtype X = X Int instance Semigroup X where Ха <> Х ь - х (аbs (a + b)) 4. O newtype X = X Int instance Semigroup X where Ха <> X ь %3D Ха
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