SOLUTION: using truth tables, decide if each argument is valid.
p ∨ ∼q
∼q → p
∴ p
Algebra.Com
Question 1151809: using truth tables, decide if each argument is valid.
p ∨ ∼q
∼q → p
∴ p
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
premise1 = p v ~q
premise2 = ~q -> p
conclusion = p
p is some logical statement that can be either true (T) or false (F)
q is also either T or F
The first two columns of the table below represent the four possible ways to have a T and F combo
The third column ~q represents the negation of column q. This is the opposite of the q column.
The fourth column has p and ~q in a disjunction. A disjunction is only false when both parts are false; otherwise, it is true.
The ~q -> p column is only false when ~q is true while p is false, ie in the form T -> F; otherwise it is true.
The last column is just a copy of the first column. It's to help set up the conclusion which is often the last column.
Truth Table
| p | q | ~q | p v ~q | ~q -> p | p |
| T | T | F | T | T | T |
| T | F | T | T | T | T |
| F | T | F | F | T | F |
| F | F | T | T | F | F |
An invalid argument would be if all the premises were true and they lead to a false conclusion. That doesn't happen here because the first two rows have a true conclusion while the last two rows have not all premises being true.
So the argument is valid.
RELATED QUESTIONS
Use truth tables to determine if the following arguments are valid.
a) p-> (q V r)
p (answered by solver91311)
I'm stuck on the following question: Use truth tables to establish whether the following... (answered by solver91311)
MAT 145: Topics In Contemporary Math
QUESTION 7
Determine if the argument is valid... (answered by Edwin McCravy,math_tutor2020)
Use truth tables to test the validity of the argument.
p → ~q
q → ~p... (answered by jim_thompson5910)
~P then q
~q then p
_________
p^q
Is this a valid argument and how to solve in a... (answered by jim_thompson5910)
Verify the following if and only if statements using truth tables:
1) ~ (P ^ Q) <=> (~P) (answered by ptfile)
In need of help!!!!
Use truth tables to test the validity of the argument.
p... (answered by Edwin McCravy)
Is this a valid argument, what is the solution.
(p→q)→r
~p V q
________
(answered by Edwin McCravy)
If p is false and q is true, determine the truth value of the following:
a) ~(p ^... (answered by Edwin McCravy,Aldorozos)