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Need help with question 8 pleaseGive a direct proof of each of the following:a) ~s, r

-> s, r | t ==> t

b) a | b, a -> c, b -> d ==> c | d

Having trouble with these 3

8. (10) Give a direct proof of each of the following:
a. -s,r - s,r vt = t
b. avb,a-c,b -d =&gt;cvd
9. (10) Give indirect proofs of each of the following:
a. -s,r - s,r vt = t
b. avb,a-c,b-d=&gt;cvd
10. (10) Is the following argument valid? If so, construct a formal proof (direct or indirect). If not,
explain why not.
If Alex gets a new job, then he will buy a guitar.
If Alex wins the lottery, then he will buy a guitar.
If Alex goes to Costa Rica, then either Alex got a new job or Alex won the lottery.
Alex goes to Costa Rica.
Therefore, Alex bought a guitar.

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