What was difficult for me?
Proof by contradiction was difficult for me. C : P ^ (~P) , (~R) => C
~R => C is true and C is false, then ~R is false and so R is true.
The syntax and the way of thinking is difficult for me. It's just a new way to go about proving something. It's fascinating to learn these different concepts of solving proofs.
However, this one is difficult for me to grasp. Even reading through the practice problems, I struggled to really grasp what is going on. I can see the parts and kind of how they fit together, but it would be difficult for me to understand - at least right now. With practice and with more practice problems I hope to be able to grasp it.
Contradiction-a combination of statements, ideas, or features of a situation that are opposed to one another
What did I find interesting?
In section 5.3, I really like being able to review the different techniques that I've been introduced to: direct proof, proof by contrapositive, proof by contradiction. As I think back on what I read, and the homework that I've already done with direct proofs and contrapositive, I can see real progression in my learning of these proofs.
I think the thing that I really find interesting about these three different proofs is that you start a proof with the end goal in mind: you know what you want to prove. There is a table on page 117 that I really like. It talks about the first step of a proof, and then with remarks/goal. I think that if I really learn the ins and outs of this table, I will be better able to go through proofs and really solve them better.
I really look forward to that.
Proof by contradiction was difficult for me. C : P ^ (~P) , (~R) => C
~R => C is true and C is false, then ~R is false and so R is true.
The syntax and the way of thinking is difficult for me. It's just a new way to go about proving something. It's fascinating to learn these different concepts of solving proofs.
However, this one is difficult for me to grasp. Even reading through the practice problems, I struggled to really grasp what is going on. I can see the parts and kind of how they fit together, but it would be difficult for me to understand - at least right now. With practice and with more practice problems I hope to be able to grasp it.
Contradiction-a combination of statements, ideas, or features of a situation that are opposed to one another
In section 5.3, I really like being able to review the different techniques that I've been introduced to: direct proof, proof by contrapositive, proof by contradiction. As I think back on what I read, and the homework that I've already done with direct proofs and contrapositive, I can see real progression in my learning of these proofs.
I also find the idea of a contradiction really interesting. I remember being a kid and learning the definition of a contradiction. When someone would say something that went against what they originally said or meant, I would smartly reply, "You are contradicting yourself." I intuitively knew what contradiction was, but now I see what it truly is and how it can be powerful in proofs and in logical thinking.
I think the thing that I really find interesting about these three different proofs is that you start a proof with the end goal in mind: you know what you want to prove. There is a table on page 117 that I really like. It talks about the first step of a proof, and then with remarks/goal. I think that if I really learn the ins and outs of this table, I will be better able to go through proofs and really solve them better.
I really look forward to that.
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