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
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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
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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