Choose the truth table and associated logic that determines whether the followin
ID: 3143133 • Letter: C
Question
Choose the truth table and associated logic that determines whether the following argment is valid:
If there is a tractor trailor accident on I-75, I-75 is blocked and highway 41 is blocked.
Highway 41 is not blocked.
Therefore, there is no tractor trailer accident on I-75.
Question options:
The argument is not valid, as the following truth table shows, where
p is "There is a tractor trailer accident on I-75"
q is "Highway 41 is blocked"
and
r is "I-75 is blocked"
p | q | r | q & r | p (q & r) | ~q | ~p
1 | 1 | 1 | 1 | 1 | 0 | 0
1 | 1 | 0 | 0 | 0 | 0 | 0
1 | 0 | 1 | 0 | 0 | 1 | 0
1 | 0 | 0 | 0 | 0 | 1 | 0
0 | 1 | 1 | 1 | 1 | 0 | 1
0 | 1 | 0 | 0 | 1 | 0 | 1
0 | 0 | 1 | 0 | 1 | 1 | 1
0 | 0 | 0 | 0 | 1 | 1 | 1
An inspection of the table above shows that every line on which ~q is true, ~p is not necessarily true as well.
The argument is not valid, as the following truth table shows, where
p is "There is a tractor trailer accident on I-75"
q is "Highway 41 is blocked"
and
r is "I-75 is blocked"
p | q | r | q & r | p (q & r) | ~q | ~p
1 | 1 | 1 | 1 | 1 | 0 | 0
1 | 1 | 0 | 0 | 0 | 1 | 0
1 | 0 | 1 | 0 | 0 | 0 | 0
1 | 0 | 0 | 0 | 0 | 1 | 0
0 | 1 | 1 | 1 | 1 | 0 | 1
0 | 1 | 0 | 0 | 1 | 1 | 1
0 | 0 | 1 | 0 | 1 | 0 | 1
0 | 0 | 0 | 0 | 1 | 1 | 1
An inspection of the table above shows that every line on which p (q & r) and ~q are true, ~p is not alwaystrue as well.
None of the above
The argument is valid, as the following truth table shows, where
p is "There is a tractor trailer accident on I-75"
q is "Highway 41 is blocked"
and
r is "I-75 is blocked"
p | q | r | q & r | p (q & r) | ~q | ~p
1 | 1 | 1 | 1 | 1 | 0 | 0
1 | 1 | 0 | 0 | 0 | 0 | 0
1 | 0 | 1 | 0 | 0 | 1 | 0
1 | 0 | 0 | 0 | 0 | 1 | 0
0 | 1 | 1 | 1 | 1 | 0 | 1
0 | 1 | 0 | 0 | 1 | 0 | 1
0 | 0 | 1 | 0 | 1 | 1 | 1
0 | 0 | 0 | 0 | 1 | 1 | 1
An inspection of the table above shows that every line on which p (q & r) and ~q are true, ~p is true as well.
The argument is not valid, as the following truth table shows, where
p is "There is a tractor trailer accident on I-75"
q is "Highway 41 is blocked"
and
r is "I-75 is blocked"
p | q | r | q & r | p (q & r) | ~q | ~p
1 | 1 | 1 | 1 | 1 | 0 | 0
1 | 1 | 0 | 0 | 0 | 0 | 0
1 | 0 | 1 | 0 | 0 | 1 | 0
1 | 0 | 0 | 0 | 0 | 1 | 0
0 | 1 | 1 | 1 | 1 | 0 | 1
0 | 1 | 0 | 0 | 1 | 0 | 1
0 | 0 | 1 | 0 | 1 | 1 | 1
0 | 0 | 0 | 0 | 1 | 1 | 1
An inspection of the table above shows that every line on which ~q is true, ~p is not necessarily true as well.
The argument is not valid, as the following truth table shows, where
p is "There is a tractor trailer accident on I-75"
q is "Highway 41 is blocked"
and
r is "I-75 is blocked"
p | q | r | q & r | p (q & r) | ~q | ~p
1 | 1 | 1 | 1 | 1 | 0 | 0
1 | 1 | 0 | 0 | 0 | 1 | 0
1 | 0 | 1 | 0 | 0 | 0 | 0
1 | 0 | 0 | 0 | 0 | 1 | 0
0 | 1 | 1 | 1 | 1 | 0 | 1
0 | 1 | 0 | 0 | 1 | 1 | 1
0 | 0 | 1 | 0 | 1 | 0 | 1
0 | 0 | 0 | 0 | 1 | 1 | 1
An inspection of the table above shows that every line on which p (q & r) and ~q are true, ~p is not alwaystrue as well.
None of the above
The argument is valid, as the following truth table shows, where
p is "There is a tractor trailer accident on I-75"
q is "Highway 41 is blocked"
and
r is "I-75 is blocked"
p | q | r | q & r | p (q & r) | ~q | ~p
1 | 1 | 1 | 1 | 1 | 0 | 0
1 | 1 | 0 | 0 | 0 | 0 | 0
1 | 0 | 1 | 0 | 0 | 1 | 0
1 | 0 | 0 | 0 | 0 | 1 | 0
0 | 1 | 1 | 1 | 1 | 0 | 1
0 | 1 | 0 | 0 | 1 | 0 | 1
0 | 0 | 1 | 0 | 1 | 1 | 1
0 | 0 | 0 | 0 | 1 | 1 | 1
An inspection of the table above shows that every line on which p (q & r) and ~q are true, ~p is true as well.
Explanation / Answer
option d
The argument is valid, as the following truth table shows, where
p is "There is a tractor trailer accident on I-75"
q is "Highway 41 is blocked"
and
r is "I-75 is blocked"
p | q | r | q & r | p (q & r) | ~q | ~p
1 | 1 | 1 | 1 | 1 | 0 | 0
1 | 1 | 0 | 0 | 0 | 0 | 0
1 | 0 | 1 | 0 | 0 | 1 | 0
1 | 0 | 0 | 0 | 0 | 1 | 0
0 | 1 | 1 | 1 | 1 | 0 | 1
0 | 1 | 0 | 0 | 1 | 0 | 1
0 | 0 | 1 | 0 | 1 | 1 | 1
0 | 0 | 0 | 0 | 1 | 1 | 1
An inspection of the table above shows that every line on which p (q & r) and ~q are true, ~