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1) Which statement is false?41 - 16b. 2 + 5710d. 1452) One way to show that the number -0.33 is rational is to show that -0.33 = xly, where x and y are integers and...

Question

1) Which statement is false?41 - 16b. 2 + 5710d. 1452) One way to show that the number -0.33 is rational is to show that -0.33 = xly, where x and y are integers and y is non-zero. Select a pair of values for x and y to show that 0.33 is rational.a.X = 33,y = 100 x = 33,y = -100 cX = 100,y = 33d.x = 100, y =-33) Select the expression that is equivalent to the following statement: Among any two consecutive positive integers , there is at least one integer that is not prime.If x is a positive integ

1) Which statement is false? 41 - 16 b. 2 + 5 710 d. 145 2) One way to show that the number -0.33 is rational is to show that -0.33 = xly, where x and y are integers and y is non-zero. Select a pair of values for x and y to show that 0.33 is rational. a.X = 33,y = 100 x = 33,y = -100 cX = 100,y = 33 d.x = 100, y =-3 3) Select the expression that is equivalent to the following statement: Among any two consecutive positive integers , there is at least one integer that is not prime. If x is a positive integer, then x is not prime or X+1 is not prime b. If x is a positive integer, then x is not prime and x+1 is not prime_ c. If x and y are positive integers, then x is not prime or y is not prime_ d. If x and y are positive integers, then x is not prime and y is not prime. 4) Select the value for x that is a counter-example to the following statement: For every integer x,x < x2 a.X = 1/2 b. X=-1/2 CX=-1 d.x=1



Answers

Determine whether each statement is true or false. a. All prime numbers are odd numbers. b. $6 \geq 6$ c. 0 is neither even nor odd. d. Every real number is a rational number.

Now we need to find whether the given statement is true or false, So the given statement is every interior is a rational number. Yeah, and this statement is true. Mhm. That is every interior is a rational number. Yes, it is true. You know that a rational number is a number which can be expressed in the form a baby where this A and we are interiors and we should be a non zero interior. Now Any interior of a can be written in the form by one where this one is not equal to zero, so any interior can be written as a ratio whose denominator is equal to one. Therefore, the statement every interior is a rational number is truth.

Okay. Is every single inter jur a rational number while integers are like negative too negative 10 12 And it continues both in the positive direction and negative direction. So all these negatives and all these positives at our whole numbers And this is true Every single integer is a rational number. I'll tell you why irrational number is a number. You can write us a fraction. So I really could put three over one. I got a fraction to everyone. I got a fraction and yeah, you've guessed I could do that for any of these. Even zero is there over 10 So all of these, even when I keep going, if we just put it over one, it's a fraction. And hence a rational number. So this is a true statement.

He guys. So our job is to see whether each of the statements given here was correct or not. So the 1st 1 every interview is a rational number. What do you guys think? Okay. For example, if I have negative nine, you can also be rewritten as negative, Benign, divided by one. Right. So this added vacio. Is that a Russian number? It is right. How about you ask to over one also a Russian number. So the first statement, it's absolutely accurate. The second statement, every whole numbers and insecurity is also true because into yours are whole numbers would negative or positive signs. Which brings us to the other statement. Every interview is a positive number, but this one is incorrect, right? It could be a knick of number two, such as negative nine. And lastly, every Russian number is an integer. Okay. For example, if I have 15/2, that right there is a Russian number, right? But 15 divided by two was 7.5 and sens a quote in 7.5 is not a whole number. It is not counted as an integer. So the last statement is incorrect. Thank you so much for listening. And they hope this house

Every integer is a rational number. Is that true, or is that false In order? Taste this question. We're gonna make a graphic. That's help us gonna group all the different kinds of real numbers and we're gonna put them into each category and specifically, we're gonna look at imagers and rational numbers and see how they're related. So we're making this graphic. We're going to start with the smallest group of numbers, and then we're just gonna get larger and larger until we've covered all the different numbers in our number system. I'm gonna go down here, so I have a little bit more room. The's smallest group of numbers are what we call natural numbers. The's air also sometimes refer to as counting numbers. And so think about when you start counting something, you start with one and then you go to 34 and then you keep counting until you've kind of everything. Natural numbers begin with the number one and go all the way to positive infinity and said natural numbers are kind of in their own group right here. One step above natural members are what we call whole numbers. Whole numbers include natural numbers As you can see, we're gonna put a little box around them, but see how there's some space outside of natural numbers. It's because there is no there are numbers that are whole numbers, but not natural numbers. Actually, there's only one, and that is the number Syria. But because whole numbers are also also natural numbers, we have zero one to three on and on and on. So as you can see some natural numbers, our whole number, we'll all national numbers are whole numbers. But there is one whole number in this case, zero. That is not a natural. Now I know you know there are more numbers than just positives, so the next step would be what we call in two years. Integers include whole numbers, natural numbers, and they also include negative numbers. As you can see, there's some extra space here that doesn't involve whole or natural numbers. So imagers start at negative infinity and they go on until we get to negative three. Negative two made 101 and then we keep going on and on. So let's review every natural number is a whole never Okay, he belongs in this category, but Once we go outside, we see that there's some space that doesn't include natural numbers such as zero. That's right. Zero What belong So zero is a whole number, but not in Africa. We keep going up when we get to integers. Notice how integers include negative numbers. So starting, like right here is what's we've added these air kind of what would exist outside of these shared groups. But then we go back to whole numbers and then also natural numbers. We can keep going. Rational numbers Is the next step rational numbers. Rational numbers are basically all the numbers in between the numbers you see on a number line. So if you think about a number line we're used to here's my zero one to negative one native to you. And then each arrow goes and goes and goes. Rational numbers are all the numbers that really fall in between right here. So definition of a rational number is any member that could be represented a fraction. So rational numbers off course include fractions, both positive and negatives. So, for example, have 1/2 negative three force. They can also be mixed fractions one and 6/7 rational numbers also include decimals. But these decimals have to be repeating, meaning there's some sort of pattern or they just have to end. So an example would be 4.2 or maybe something like 3.7 repeating. And then one more example. Rational number would be something like this Larry before, because one once we sim simplify that scared of forest, too, and too is just a fraction because it's to over one. Now there's one more other category. Do this and outside. Um, rational numbers is you irrational numbers. Irrational numbers are basically not the pretty ones. They're decimals that don't ever end that go on and on and also do not have any sort of pattern. An example of that would be pai. We know that pie stands for decimal that never ends and never repeats. There's no pattern. An example of one of those would be, And I'm just gonna make this up. 7.2963 dot dot, dot, dot dot. As you can see, we can't guess what comes next. So this is an example of an irrational number. Another one would be square root of seven because the square to 77 is not a perfect square. So seven is not scared of seven is irrational. So after all this, what? What all these categories mean? What does this group mean? I'm gonna race this. I have a little bit more room. What All this means is all of this right here. Rational editors. Whole numbers. Natural numbers in the Russian members are all part of what we call riel numbers. Okay, So anything that's a real number is going to be in this category and all of these cover all of the numbers out. Lena. So let's go back up to her question. Every integer is a rational number. Is that true, or is that false? So for looking at our imager category, who is he underneath? He is underneath the rational numbers. That means every single imager belongs in the rational number. So every integer is a rational number. That's true.


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