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IIL Symbolize the following statements in quantificational logic using the symbol keys provided1. Plato and Aristotle were philosophers_ (a: Aristotle; p: Plato; P(...

Question

IIL Symbolize the following statements in quantificational logic using the symbol keys provided1. Plato and Aristotle were philosophers_ (a: Aristotle; p: Plato; P(x): x is a philosopher)2. No sodas are caffeine-free (C(x): x is caffeine-= ~ftee; S(x): x is a soda)3 . Every dog likes Johnny. (j: Johnny; D(x): x is a dog: L(x, y): x likes y)4. Iris has an aunt (i: Tris; A(X, y): x is an aunt ofy)

IIL Symbolize the following statements in quantificational logic using the symbol keys provided 1. Plato and Aristotle were philosophers_ (a: Aristotle; p: Plato; P(x): x is a philosopher) 2. No sodas are caffeine-free (C(x): x is caffeine-= ~ftee; S(x): x is a soda) 3 . Every dog likes Johnny. (j: Johnny; D(x): x is a dog: L(x, y): x likes y) 4. Iris has an aunt (i: Tris; A(X, y): x is an aunt ofy)



Answers

In some approaches to logic, the only connectives are $\sim$ and $\rightarrow$ and the other logical connectives are defined in terms of these.* Verify this by using a truth table to demonstrate the following equivalences.
$$p \vee q \equiv \sim p \rightarrow q$$

Okay, so it's all for 1/3 column. That's Pete and Q. So that's true. Fourth, false and forced. And now let's find our in negation of you That's false. True, false and true are we? Write our column of P here and now. Let's find our conditional between these two. So this is false and everything else is true. And now let's negate that our blue coal working in the gate or book on That's true, false, false and force, and we see that this column is a call in to this one.

Hello. Welcome to this lesson in this lesson. US person. The that the the largest, as negations of themselves. So here we have for some Z for all y for all X for the project. Katie of X, Y and Z. Yes, President. US delegation. So here. Still we will not touch the domain. All of them would be in the same domain by here. The statement or the project. Kate would become negative of war. He used to be okay. All right, so And if the negation follows the Project eight Okay, so All right, that's the negation. Oh, the next one is local of this for for certain X for certain y for the project p of excellent y and for certain for all x for all y For certain educate care of x and y so here because he had and and we want to negate it would negate board project Kate so that the and would become negative of what used to be. Okay. So, for example, if we're looking for the height, that is a plus X plus y and X plus two y now would be having the opposite of both of them individually. Okay, so here becomes for some X for some y of the project eight p of x and y negation. We negate the per educate and for us for all y we negate the per educates. Mm. Okay, so that is just for B. Let's go to the sea. Bad. Okay, so for all for some X for some. Why? For the project, Kate. Tale of x and y, by implication do in the gates. Mhm. They kill. Okay, So that the K would now by implicate the negative of itself. Okay, He used to By implicating yourself. Now, by implicates, they are, by implication of their negatives. Let me put it that way. Okay? Yeah. So the by implication of the negatives this by implicates it's negative. All right, so it means it has been negated. Let's go to the final one. Okay. Where we have the all so for why? For some X for some Z, both the the 90 gets the pre Lucchetti of X, y and Z or 90 gets the care for X and y Okay, so this is the negation of that. Okay, so thanks your time. That's the end of the lesson.

Hey, it's clear. So a new range. So for part eight, we're gonna express the negation of the statement. So we're given I'll just put the negation sign in front t of X. Why? I see we're gonna use the dim organs law for qualifiers three times and you end up getting existential, not tea of X y Z for part B. We're gonna use dum organs law. So we start off with thinning negation. Uh, this statement p of x y or universal q of X y used to Morgan's law to simplify X Y and not universal q X y. And we used to Morgan slow for qualifiers. I should put the equivalent simple Universal not he of X y and Texas 10 Show Universal not of Q. Next. Why for part c. We're doing the negation of the given statement p of x y and existential. Next Waas. See, we're gonna use the Morgans law for qualifiers and we got not p of X, my and existential X y Z, and we used to Morgan's law or not exist on show of X. Why see and finally muse to Morgan's law for qualifiers, not P of X y or universal? No, our of Why, that's why I see then for party. We need the negation of the statement p of x lie, then Q of X y we're gonna use to Morgan's law for qualifiers, then Q of X y finally muse logical equivalents. This is a universal symbol p of X y and not Q. Of X Y.


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