Is the following valid or invalid? (show by using a truth table).
If Rick gains employment, then Rick will earn a paycheck. p->q
If Rick earns a paycheck, then Rick will be excited. q->r
Rick gains employment. p
____________________________
Rick will be excited. r
what is my final statement? Which is correct before completing my truth table?
[p^(p->q)]^(q->r) or is it [p^(p->q)]^r
Hello, CPR!
Is the following valid or invalid? (show by using a truth table).
If Rick gains employment, then Rick will earn a paycheck. .
If Rick earns a paycheck, then Rick will be excited. .
Rick gains employment. .
-----------------------------------------------
Therefore: Rick will be excited. .
The argument is: .
(The argument is valid; the final column should be eight T's.)
Thanks for the help. I got it. I was on the right page. Perhaps you can help me with my post under Urgent Help. It is an Induction problem.
It is 1+2+3....(4n-2)= n(3n-1)
The basic step is n=1. 4(1)-2 = 1(3(1)-1)
Induction step is:
1+2+3....(4k-2) = k(3k-1)
1+2+3....(4k-2)+(k+1) = k(3k-1) = (K+1)
I'm having problems from this point. Please help!
you want to prove:
1+2+3....(4k-1) = (k+1)(3k)
which equals
1+2+3....(4k-1) = (3k^2 + 3k)
So now rather than try to simplify it any further (like you did above), you need to prove that (4k-1) = (3k^2+3k)...so start from the left, and try to get the right. Don't start with what you want to prove..You will need to suppose that (4k-2) = k(3k-1) (This is your IH) and use it to prove k+1, so in your algebra, you want to get 4k-2, so you can say "I know that 4k-2 = k(3k-1) and therefore...blah blah blah"
Use that and do the algebra to get (4k-1) = (3k^2+3k), don't forget about your IH which you'll need to complete the proof.