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.