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Consider the operation a ∗ b = a + b − 3 onthe set Q ofrational numbers. Which of the following is a correct argument (meaning that boththe statement an...

Question

Consider the operation a ∗ b = a + b − 3 onthe set Q ofrational numbers. Which of the following is a correct argument (meaning that boththe statement and its proof are correct)? Select all thatapply.

Consider the operation a ∗ b = a + b − 3 on the set Q of rational numbers. Which of the following is a correct argument (meaning that both the statement and its proof are correct)? Select all that apply.



Answers

Prove or disprove that if $a$ and $b$ are rational numbers, then $a^{b}$ is also rational.

But I would like to look at the expression No weapons allowed here. A minus B over. Be minus a. So we're gonna simplify this expression. Only the top alone and make it a minus bi then on the bottom. I'm gonna take out a negative one out of this expression. So if I did that, I was gonna multiply that negative one through there. Then this would make this in native be plus today, which could be rewritten by just rearranging those letters would still leave that top alone. And we have that negative one out here and it would be a minus b. So again, with simplifying now we have a minus bi neighbors be We could simplify that. Then we have one over a negative one. We should be the same thing, This negative one. So this expression here simplified could be also written as negative one

It's a part A. We have a Manistee all over B minus a. So we're gonna simplify the bottom. Sorto, take out a negative one. So we have a negative beating and then a minus bi. So that cancels so well. That's with negative one. So for being in the simplified, this a minus bi all over a minus bi that just cancels and make positive one. Therefore, see a plus B all over a minus. Bi, you cannot simplify this that this is the only one so far. D the minus a all over b plus a again. You can't not simplify this office.

In this problem, I'm going to take some statements and use my real number systems diagram to determine if the statements are true we're not. So here's my diagram. I've got natural whole integers rational, irrational and real numbers all in one organizational tool. So this first statement says that all integers are natural numbers. So all integers this box here. Everything inside this box is also inside the natural number box. And this is not true because I've got some integer numbers that are not highlighted double and they would have to be highlighted double to both be true. So this is false. Okay, the second statement, all rational numbers are real numbers. So all rational numbers. Everything inside this big box is also located in this real. That is very true because we have highlighted the rational numbers twice. Okay, our next one is all natural numbers are rational numbers. So all natural numbers. This little box are also located inside the rational number box. And this is also true because our natural numbers are labeled or highlighted twice.

So in the given question we have a rational expression that has given us a X plus b, X plus b times three x plus two. And it is given that the zeros of this polynomial Zeros of this racial expression is given as -2 x three and one x 2. So when we equate this expression to zero, we can write that three X plus two is equal to zero from which we can write X as then equal to minus two by three which we have over here. And similarly we can equip a X plus B equal to zero from which we can write X is equal to minus B by here. So the other route that has been given the question is one by two. So we can combat minus B by a 21 by two from which we would get A. Is equal to minus of to be right. In the question, what we are told to find is the sum of a plus B. Right? So is equal to minus to be. So we would have minus to B plus B, which is equal to minus B. So this is the required answer. I hope you understood the method. Thank you.


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