Let the following statements be given. p= "You can vote." q= "You are under 18 years old." r = "You are from Mars." (a) Translate the following statement into symbols of formal logic. You can't vote if you are under 18 years old or you are from Mars. O (qvr) → p Op → (q^r) O(q^r) → p O (qvr) → p O-p → (q Vr) (b) Give the contrapositive of this statement in the symbols of formal logic. Op → ¬(q^r) O¬¬p → ¬(q Vr) O¬p → ¬(q vr) O-(q vr) →→P O(q^r) →→P (c) Give the contrapositive in English. O If you are under 18, then you can't vote nor are you from Mars. O If you are not under 18 nor are you from Mars, then you can't vote. O If you can't vote, then you are not under 18 nor are you from Mars. O If you can vote, then you are not under 18 nor are you from Mars. O If you are not under 18 nor are you from Mars, then you can vote.
Let the following statements be given. p= "You can vote." q= "You are under 18 years old." r = "You are from Mars." (a) Translate the following statement into symbols of formal logic. You can't vote if you are under 18 years old or you are from Mars. O (qvr) → p Op → (q^r) O(q^r) → p O (qvr) → p O-p → (q Vr) (b) Give the contrapositive of this statement in the symbols of formal logic. Op → ¬(q^r) O¬¬p → ¬(q Vr) O¬p → ¬(q vr) O-(q vr) →→P O(q^r) →→P (c) Give the contrapositive in English. O If you are under 18, then you can't vote nor are you from Mars. O If you are not under 18 nor are you from Mars, then you can't vote. O If you can't vote, then you are not under 18 nor are you from Mars. O If you can vote, then you are not under 18 nor are you from Mars. O If you are not under 18 nor are you from Mars, then you can vote.
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
![Let the following statements be given.
p= "You can vote."
q = "You are under 18 years old."
r = "You are from Mars."
(a) Translate the following statement into symbols of formal logic.
You can't vote if you are under 18 years old or you are from Mars.
O (q vr) → p
O¬p → (q^r)
O (q^r) → p
O (qvr) → p
O¬p → (qVr)
(b) Give the contrapositive of this statement in the symbols of formal logic.
Op
(q^r)
O¬¬p → ¬(q V r)
O¬p → ¬(q Vr)
(q V r) →
O(g ^r) →
p
p
(c) Give the contrapositive in English.
O If you are under 18, then you can't vote nor are you from Mars.
O If you are not under 18 nor are you from Mars, then you can't vote.
O If you can't vote, then you are not under 18 nor are you from Mars.
O If you can vote, then you are not under 18 nor are you from Mars.
O If you are not under 18 nor are you from Mars, then you can vote.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92b516fe-d53b-47c4-98a0-9a769a93d27e%2F20d27137-6d27-4116-b2fd-5039e65c7f0f%2F7tui4pk_processed.png&w=3840&q=75)
Transcribed Image Text:Let the following statements be given.
p= "You can vote."
q = "You are under 18 years old."
r = "You are from Mars."
(a) Translate the following statement into symbols of formal logic.
You can't vote if you are under 18 years old or you are from Mars.
O (q vr) → p
O¬p → (q^r)
O (q^r) → p
O (qvr) → p
O¬p → (qVr)
(b) Give the contrapositive of this statement in the symbols of formal logic.
Op
(q^r)
O¬¬p → ¬(q V r)
O¬p → ¬(q Vr)
(q V r) →
O(g ^r) →
p
p
(c) Give the contrapositive in English.
O If you are under 18, then you can't vote nor are you from Mars.
O If you are not under 18 nor are you from Mars, then you can't vote.
O If you can't vote, then you are not under 18 nor are you from Mars.
O If you can vote, then you are not under 18 nor are you from Mars.
O If you are not under 18 nor are you from Mars, then you can vote.
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