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Identify the correct translation into logical notation of the following assertion.
“You can not ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old.”
Where q = “You can ride the roller coaster”
r = “You are under 4 feet tall”
s = “You are older than 16 years old”
- a)q→(r∧-s)
- b)q→(r∨-s)
- c)(r∧=s)→-q
- d)(r∧-s)→q
Correct answer is option 'C'. Can you explain this answer?
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Identify the correct translation into logical notation of the followi...
A à B can be represented like B if A.
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The third option seems the most appropriate as ~Q is on the right-hand side.
(r∧= s)→-q . If you try to interpret this mathematical statement, you will get that this is the most appropriate.
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Identify the correct translation into logical notation of the followi...
Translation of the assertion into logical notation:
The given assertion can be broken down into two parts:
1. If you are under 4 feet tall and older than 16 years old, then you can ride the roller coaster.
2. If you are under 4 feet tall and not older than 16 years old, then you cannot ride the roller coaster.
Let's translate these two parts into logical notation using the given propositions:
q = "You can ride the roller coaster"
r = "You are under 4 feet tall"
s = "You are older than 16 years old"
Translation of the first part:
"If you are under 4 feet tall and older than 16 years old, then you can ride the roller coaster."
This can be written as: (r ∧ s) → q
Translation of the second part:
"If you are under 4 feet tall and not older than 16 years old, then you cannot ride the roller coaster."
This can be written as: (r ∧ ¬s) → ¬q
Combining the translations:
From the two parts, we can combine the translations using logical OR (represented by ∨) because either of the conditions can result in the same conclusion. The correct translation of the given assertion is:
(q → ((r ∧ s) ∨ (r ∧ ¬s)))
Explanation:
The correct translation (c) represents the given assertion accurately. It states that if you can ride the roller coaster (q), then either you are under 4 feet tall and older than 16 years old (r ∧ s), or you are under 4 feet tall and not older than 16 years old (r ∧ ¬s).
This translation captures the condition that you cannot ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old. It covers both parts of the assertion and represents the logical relationship between the propositions correctly.
The given assertion can be broken down into two parts:
1. If you are under 4 feet tall and older than 16 years old, then you can ride the roller coaster.
2. If you are under 4 feet tall and not older than 16 years old, then you cannot ride the roller coaster.
Let's translate these two parts into logical notation using the given propositions:
q = "You can ride the roller coaster"
r = "You are under 4 feet tall"
s = "You are older than 16 years old"
Translation of the first part:
"If you are under 4 feet tall and older than 16 years old, then you can ride the roller coaster."
This can be written as: (r ∧ s) → q
Translation of the second part:
"If you are under 4 feet tall and not older than 16 years old, then you cannot ride the roller coaster."
This can be written as: (r ∧ ¬s) → ¬q
Combining the translations:
From the two parts, we can combine the translations using logical OR (represented by ∨) because either of the conditions can result in the same conclusion. The correct translation of the given assertion is:
(q → ((r ∧ s) ∨ (r ∧ ¬s)))
Explanation:
The correct translation (c) represents the given assertion accurately. It states that if you can ride the roller coaster (q), then either you are under 4 feet tall and older than 16 years old (r ∧ s), or you are under 4 feet tall and not older than 16 years old (r ∧ ¬s).
This translation captures the condition that you cannot ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old. It covers both parts of the assertion and represents the logical relationship between the propositions correctly.
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Identify the correct translation into logical notation of the following assertion.“You can not ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old.”Where q = “You can ride the roller coaster”r = “You are under 4 feet tall”s = “You are older than 16 years old”a)q→(r∧-s)b)q→(r∨-s)c)(r∧=s)→-qd)(r∧-s)→qCorrect answer is option 'C'. Can you explain this answer?
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Identify the correct translation into logical notation of the following assertion.“You can not ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old.”Where q = “You can ride the roller coaster”r = “You are under 4 feet tall”s = “You are older than 16 years old”a)q→(r∧-s)b)q→(r∨-s)c)(r∧=s)→-qd)(r∧-s)→qCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Identify the correct translation into logical notation of the following assertion.“You can not ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old.”Where q = “You can ride the roller coaster”r = “You are under 4 feet tall”s = “You are older than 16 years old”a)q→(r∧-s)b)q→(r∨-s)c)(r∧=s)→-qd)(r∧-s)→qCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Identify the correct translation into logical notation of the following assertion.“You can not ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old.”Where q = “You can ride the roller coaster”r = “You are under 4 feet tall”s = “You are older than 16 years old”a)q→(r∧-s)b)q→(r∨-s)c)(r∧=s)→-qd)(r∧-s)→qCorrect answer is option 'C'. Can you explain this answer?.
Identify the correct translation into logical notation of the following assertion.“You can not ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old.”Where q = “You can ride the roller coaster”r = “You are under 4 feet tall”s = “You are older than 16 years old”a)q→(r∧-s)b)q→(r∨-s)c)(r∧=s)→-qd)(r∧-s)→qCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Identify the correct translation into logical notation of the following assertion.“You can not ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old.”Where q = “You can ride the roller coaster”r = “You are under 4 feet tall”s = “You are older than 16 years old”a)q→(r∧-s)b)q→(r∨-s)c)(r∧=s)→-qd)(r∧-s)→qCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Identify the correct translation into logical notation of the following assertion.“You can not ride the roller coaster if you are under 4 feet tall unless you are older than 16 years old.”Where q = “You can ride the roller coaster”r = “You are under 4 feet tall”s = “You are older than 16 years old”a)q→(r∧-s)b)q→(r∨-s)c)(r∧=s)→-qd)(r∧-s)→qCorrect answer is option 'C'. Can you explain this answer?.
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