What did I find difficult?
The most problematic part of the reading was quantified statements. Reading through the examples was tough for me. You have both the universal quantifier, which is an upside down capital A. Then you have the existential quantifier which is a backwards capital E. Universal quantifiers can be read as for every. Existential quantifiers can be read as there exists.
I think this part of the reading was difficult for me because it was new. Even after reading through the chapter and the numerous examples, I still have a few questions about these quantifiers. I understand that "the universal quantifier is used to claim that the statement resulting from a given open sentence is true when each value of the domain of the variable is assigned to the variable."
We also have the existential quantifier, which "is used to claim that at least one statement resulting from a given open sentence is true when the values of a variable are assigned from its domain."
After some reading and explanation, I understand the simple uses of both universal and existential quantifiers, but when the reading got to quantified statements involving two variables, that was difficult for me to wrap my head around. Then, the book left me nervous, talking about when a quantified statement may contain both universal and existential quantifiers! Good thing that is not until Section 7.2!
What did I find interesting?
I love these laws:
1. Commutative laws
2. Associative laws
3. Distributive laws
4. De Morgan's laws
I really like De Morgan's law. For some reason I can picture it really well. The negation of the disjunction of P and Q is the conjunction of the negation of both P and Q. I can picture that in my head, and I can see how it would be useful for solving problems. It's a different way of looking at how to solve problems such as these proofs. Even more importantly, I think these laws teach a fundamental principle of taking a step back, evaluating the situation at hand, and then seeing if you can see a problem you are facing in a different light. If you can, you should try and attack it from that different angle. Just like these laws open up a whole slew of new possibilities in solving mathematical proofs, taking a step back and reevaluating can help greatly with problems we face in life.
I also really like quantified statements despite the trouble they are giving me. First looking at the symbols, I was confused at how to go about using them. Then I read more about them and it makes sense. I see the purpose in changing open sentences into statements, especially in a proofs class such as this.
The most problematic part of the reading was quantified statements. Reading through the examples was tough for me. You have both the universal quantifier, which is an upside down capital A. Then you have the existential quantifier which is a backwards capital E. Universal quantifiers can be read as for every. Existential quantifiers can be read as there exists.
I think this part of the reading was difficult for me because it was new. Even after reading through the chapter and the numerous examples, I still have a few questions about these quantifiers. I understand that "the universal quantifier is used to claim that the statement resulting from a given open sentence is true when each value of the domain of the variable is assigned to the variable."
We also have the existential quantifier, which "is used to claim that at least one statement resulting from a given open sentence is true when the values of a variable are assigned from its domain."
After some reading and explanation, I understand the simple uses of both universal and existential quantifiers, but when the reading got to quantified statements involving two variables, that was difficult for me to wrap my head around. Then, the book left me nervous, talking about when a quantified statement may contain both universal and existential quantifiers! Good thing that is not until Section 7.2!
What did I find interesting?
I love these laws:
1. Commutative laws
2. Associative laws
3. Distributive laws
4. De Morgan's laws
I really like De Morgan's law. For some reason I can picture it really well. The negation of the disjunction of P and Q is the conjunction of the negation of both P and Q. I can picture that in my head, and I can see how it would be useful for solving problems. It's a different way of looking at how to solve problems such as these proofs. Even more importantly, I think these laws teach a fundamental principle of taking a step back, evaluating the situation at hand, and then seeing if you can see a problem you are facing in a different light. If you can, you should try and attack it from that different angle. Just like these laws open up a whole slew of new possibilities in solving mathematical proofs, taking a step back and reevaluating can help greatly with problems we face in life.
I also really like quantified statements despite the trouble they are giving me. First looking at the symbols, I was confused at how to go about using them. Then I read more about them and it makes sense. I see the purpose in changing open sentences into statements, especially in a proofs class such as this.
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