COS3761
Assignment 1
2023
Unique No.: 523317
Due date: 25 May 2023
Please note: This document should only be used as a guide for your own assignment. We do
not condone plagiarism.
www.tutorialspoint.com
, Solution:
The correct propositional logic translation of the given English sentence is Option 4:
(s ∧ r) → (p ∨ t).
Explanation: Let's break down the given English sentence using propositional logic
symbols:
• Let s be "The economy is weak"
• Let r be "The party leader is a populist"
• Let p be "My party wins the election"
• Let t be "The voter turnout is low"
The sentence can be represented as: (s ∧ r) → (p ∨ t), which translates to "If the
economy is weak and the party leader is a populist, then either my party wins the
election or the voter turnout is low."
Explanation:
Option 1: (p ∨ t) → (s ∧ r) - This option is incorrect as it represents the converse of
the given sentence, which is not equivalent to the original sentence.
Option 2: (s ∨ r) → (p ∧ t) - This option is incorrect as it represents a different
statement altogether, which is not equivalent to the original sentence.
Option 3: (p ∧ t) → (s ∨ r) - This option is incorrect as it represents the inverse of the
given sentence, which is not equivalent to the original sentence.
www.tutorialspoint.com
, Explanation:
The sentence can be represented as a conditional statement "if-then" with a
conjunction "and" in the consequent. In propositional logic, "if-then" is represented
as → and "and" is represented as ∧.
"The voter turnout is low only if both the economy is strong and the party
leader isn't a populist"
Therefore, the given sentence can be translated as t→(¬s∧¬r).
The option 1 is incorrect because it translates the sentence as "If the voter turnout
is low, then the economy is weak and the party leader is a populist and the party
leader is not a populist," which is not equivalent to the original sentence.
Option 3 is incorrect because it translates the sentence as "If the economy is
strong and the party leader is a populist, then the voter turnout is low," which is not
equivalent to the original sentence.
Option 4 is incorrect because it translates the sentence as "If the economy is not
weak, then the voter turnout is high, and if the party leader is not a populist, then
the voter turnout is high," which is not equivalent to the original sentence.
www.tutorialspoint.com
Assignment 1
2023
Unique No.: 523317
Due date: 25 May 2023
Please note: This document should only be used as a guide for your own assignment. We do
not condone plagiarism.
www.tutorialspoint.com
, Solution:
The correct propositional logic translation of the given English sentence is Option 4:
(s ∧ r) → (p ∨ t).
Explanation: Let's break down the given English sentence using propositional logic
symbols:
• Let s be "The economy is weak"
• Let r be "The party leader is a populist"
• Let p be "My party wins the election"
• Let t be "The voter turnout is low"
The sentence can be represented as: (s ∧ r) → (p ∨ t), which translates to "If the
economy is weak and the party leader is a populist, then either my party wins the
election or the voter turnout is low."
Explanation:
Option 1: (p ∨ t) → (s ∧ r) - This option is incorrect as it represents the converse of
the given sentence, which is not equivalent to the original sentence.
Option 2: (s ∨ r) → (p ∧ t) - This option is incorrect as it represents a different
statement altogether, which is not equivalent to the original sentence.
Option 3: (p ∧ t) → (s ∨ r) - This option is incorrect as it represents the inverse of the
given sentence, which is not equivalent to the original sentence.
www.tutorialspoint.com
, Explanation:
The sentence can be represented as a conditional statement "if-then" with a
conjunction "and" in the consequent. In propositional logic, "if-then" is represented
as → and "and" is represented as ∧.
"The voter turnout is low only if both the economy is strong and the party
leader isn't a populist"
Therefore, the given sentence can be translated as t→(¬s∧¬r).
The option 1 is incorrect because it translates the sentence as "If the voter turnout
is low, then the economy is weak and the party leader is a populist and the party
leader is not a populist," which is not equivalent to the original sentence.
Option 3 is incorrect because it translates the sentence as "If the economy is
strong and the party leader is a populist, then the voter turnout is low," which is not
equivalent to the original sentence.
Option 4 is incorrect because it translates the sentence as "If the economy is not
weak, then the voter turnout is high, and if the party leader is not a populist, then
the voter turnout is high," which is not equivalent to the original sentence.
www.tutorialspoint.com
