6. Using truth tables determines whether the argument is valid or invalid. 1. If a human being can be in two places at the same time, he must be with you. I'm not with you. A human being cannot be in two places at the same time. 2. If my check arrives on time, I sign up for the next term. I signed up for the next term. My check arrived on time
6. Using truth tables determines whether the argument is valid or invalid. 1. If a human being can be in two places at the same time, he must be with you. I'm not with you. A human being cannot be in two places at the same time. 2. If my check arrives on time, I sign up for the next term. I signed up for the next term. My check arrived on time
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:6.
Using truth tables determines whether the argument is valid or invalid.
1.
If a human being can be in two places at the same time, he must be with you.
I'm not with you.
A human being cannot be in two places at the same time.
2.
If my check arrives on time, I sign up for the next term.
I signed up for the next term.
My check arrived on time
Expert Solution
Step 1
Given:
The argument,
If a human being can be in two places at the same time, he must be with you.
I'm not with you.
A human being cannot be in two places at the same time.
Step 2
Let p: A human being can be in two places at the same time.
q: he must be with you.
r: I'm with you.
Therefore, symbolically the argument can be written as
p → q
~ r
--------
~p
Step 3
The truth table is given by
| p | q | r | ~r | p → q | (p → q)⋀~r | ~p | [(p → q)⋀~r]→~p |
| T | T | T | F | T | F | F | T |
| T | T | F | T | T | T | F | F |
| T | F | T | F | F | F | F | T |
| T | F | F | T | F | F | F | T |
| F | T | T | F | T | F | T | T |
| F | T | F | T | T | T | T | T |
| F | F | T | F | T | F | T | T |
| F | F | F | T | T | T | T | T |
Thus the given argument is not valid.
Step 4
Given:
The given argument is,
If my check arrives on time, I sign up for the next term.
I signed up for the next term.
My check arrived on time.
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