SOLUTION: I am not the brightest crayon in the box when it comes to algebra, but this stuff is horrific!. Please help me. It is for homework... 6. (a) Translate the argument into symb

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Question 192750: I am not the brightest crayon in the box when it comes to algebra, but this stuff is horrific!. Please help me. It is for homework...
6. (a) Translate the argument into symbolic form and (b) determine if the argument is valid or invalid. You may compare the argument to a standard form or use a truth table.
If it is raining, then we will close the window.
We closed the window.
----------------------------------------------------------------------
∴ It is raining.
It appears to be a valid statement to me. I just can not translate into symbolic form.

Found 2 solutions by user_dude2008, Mathtut:
Answer by user_dude2008(1862) (Show Source):
You can put this solution on YOUR website!
p: It is raining
q: We will close the window

Symbolic Form:

p -> q
q
-------
therefore p

Truth Table:

p q p -> q q p
T T T T T
T F F F T
F T T T F
F F T F F

premises - red, conclusion - blue

Look at line 3 in table: all true premises but false conclusion

Answer: argument is invalid

Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!

The only thing promised in this condition statement is that if it is raining then we will close the window
:
just because we close the window doesnt necessarily mean it is raining. It might or might not be raining
:
basically if p is the statement it is raining and q is we will close the window
:
We are given... if p then q or p->q. We are asked does q -> p
truth table
:
p q (p->q) -> (q->p)
______________________
T T T T T
T F F T T
F T T F F
F F T T T
:
therefore the statement is invalid