Use truth tables to determine whether the following argument is valid: If there is a tractor trailor accident on I-75, highway 41 is blocked. Highway 41 is blocked. Therefore, there is a tractor trailer accident on I-75.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 | 1An 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.