Discrete Math Use a truth table to determine if the given argument form is valid.

Phoebe

Phoebe

Answered question

2021-08-12

Discrete Math
Use a truth table to determine if the given argument form is valid.
pq
rp
qr
q

Answer & Explanation

davonliefI

davonliefI

Skilled2021-08-13Added 79 answers

Step 1
An argument is valid if the rows with all the premises are true, then the conclusion must also be true.
If any rows with all the premises are true contains a false conclusion, then the statement is invalid.
Here, the argument is,
pq
rp
qr
q
The premises are ,
pq
rp
qr
The conclusion is q.
Step 2
The truth table of the premises and conclusion is as follows.
pqrpqrpqrq(conclusion)TTTTTTTTTFTTTTTFTFTTTTFFFTFFFTTTFTFFTFTTTTFFTTFTTFFFTTFF
Step 3
Here, all the critical rows (rows with contain only true in premises) has the conclusion true.
That is, all the premises are true, then the conclusion is also true.
Therefore, the given argument is valid.

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