# Thread: valid or invalid ?

1. ## valid or invalid ?

Determine whether the following argument of this form is a valid or an invalid using the truth table:

If I am student and I am not reading then I will go to the birth day party.
I am student or I am reading.
If it is reading then I am student.
Therefore I will go to the birth day party

2. Hello, naseerhaider!

I'll get you started . . .

Determine whether the following argument of this form is a valid or an invalid using the truth table:

[1] If I am a student and I am not reading, then I will go to the birthday party.
[2] I am student or I am reading.
[3] If I am reading then. I am a student.
[4] Therefore I will go to the birthday party
$\displaystyle p$: I am a student.
$\displaystyle q$: I am reading.
$\displaystyle r$: I will go to the birthday party.

Statement [1] is: .$\displaystyle (p\: \wedge \sim\!q) \to r$

Statement [2] is: .$\displaystyle p \vee q$

Statement [3] is: .$\displaystyle q \to p$

Statement [4] is: .$\displaystyle r$

The statement to test in a truth table is:

. . $\displaystyle \bigg(\left[(p\,\wedge \sim\!q) \to r\right] \:\wedge\: (p \vee q) \:\wedge \:(q \to p)\bigg) \;\to\; r$

3. Originally Posted by Soroban
Hello, naseerhaider!

I'll get you started . . .

$\displaystyle p$: I am a student.
$\displaystyle q$: I am reading.
$\displaystyle r$: I will go to the birthday party.

Statement [1] is: .$\displaystyle (p\: \wedge \sim\!q) \to r$

Statement [2] is: .$\displaystyle p \vee q$

Statement [3] is: .$\displaystyle q \to p$

Statement [4] is: .$\displaystyle r$

The statement to test in a truth table is:

. . $\displaystyle \bigg(\left[(p\,\wedge \sim\!q) \to r\right] \:\wedge\: (p \vee q) \:\wedge \q \to p)\bigg) \;\to\; r$

Thanks a lot buddy.relay great job