Consider the following argument: If I am vaccinated, then I will not contract measles. If I contract measles then I will die, I am not vaccinated. Therefore, I will die. Define the propositions: I will die. I contract measles. I am vaccinated. d: m: V: (a) Rewrite the argument in symbols. (b) Construct a truth table with a column for each premise and for the conclusion. d m v (c) State whether or not the argument is valid and give the reason why.

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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the quetion is below, im finding it hard to undertsand the topic

Consider the following argument:
If I am vaccinated, then I will not contract measles.
If I contract measles then I will die,
I am not vaccinated.
Therefore, I will die.
Define the propositions:
I will die.
I contract measles.
I am vaccinated.
d:
m:
V:
(a)
Rewrite the argument in symbols.
(b)
Construct a truth table with a column for each premise and for the conclusion.
d m v
(c)
State whether or not the argument is valid and give the reason why.
Transcribed Image Text:Consider the following argument: If I am vaccinated, then I will not contract measles. If I contract measles then I will die, I am not vaccinated. Therefore, I will die. Define the propositions: I will die. I contract measles. I am vaccinated. d: m: V: (a) Rewrite the argument in symbols. (b) Construct a truth table with a column for each premise and for the conclusion. d m v (c) State whether or not the argument is valid and give the reason why.
Expert Solution
Step 1

a. The arguments can be written in symbols as follows:

v → ~m       (vaccinated implies no measles)      (premise)

m → d          (measles implies dies)                     (premise)

~v                (not vaccinated)                               (premise)

∴ d              (therefore die)                                  (conclusion)

Step 2

The following truth tables will help in filling the premises and conclusion truth table:

a → b

a b a → b
T
T
F
F
T
F
T
F
T
F
T
T

a → ~b

a b a → ~b
T
T
F
F
T
F
T
F
F
T
T
T
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