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cashflow
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I took a quiz that I was very confident in and just got the scores back today -- I did terribly (50%). Anyway, I am trying to understand where my mistake is below. I went over this three times and I cannot figure out why it's wrong (it looks right to me).
To Prove: ~(p ∧ r) ∨ ~(q ∨ r) ≡ p ∧ r → ~r ∧ ~q
First, we know that a ≡ b is the same as b ≡ a. So, in my case, I started with b and worked to prove a.
Proof:
Starting with:
p ∧ r → ~r ∧ ~q
≡ ~(p ∧ r) ∨ (~r ∧ ~q) by the '∨' def. of '→'
≡ ~(p ∧ r) ∨ ~(r ∨ q) by De Morgan's Law
≡ ~(p ∧ r) ∨ ~(q ∨ r) by Commutative Law
I asked the professor where, and he said "It doesn't matter where. I looked at it and saw this lacked quality." I don't understand. I proved that the two sides are the logically equivalent in 3 steps. Help please? Thank you!
To Prove: ~(p ∧ r) ∨ ~(q ∨ r) ≡ p ∧ r → ~r ∧ ~q
First, we know that a ≡ b is the same as b ≡ a. So, in my case, I started with b and worked to prove a.
Proof:
Starting with:
p ∧ r → ~r ∧ ~q
≡ ~(p ∧ r) ∨ (~r ∧ ~q) by the '∨' def. of '→'
≡ ~(p ∧ r) ∨ ~(r ∨ q) by De Morgan's Law
≡ ~(p ∧ r) ∨ ~(q ∨ r) by Commutative Law
I asked the professor where, and he said "It doesn't matter where. I looked at it and saw this lacked quality." I don't understand. I proved that the two sides are the logically equivalent in 3 steps. Help please? Thank you!