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Find a function from the interval (3,10) to the interval (2,7)which is a one-to-one correspondence between these two sets. Showthat your function is both one-to-one...

Question

Find a function from the interval (3,10) to the interval (2,7)which is a one-to-one correspondence between these two sets. Showthat your function is both one-to-one and onto. What does this sayabout the cardinality of both of these sets?

Find a function from the interval (3,10) to the interval (2,7) which is a one-to-one correspondence between these two sets. Show that your function is both one-to-one and onto. What does this say about the cardinality of both of these sets?



Answers

If a relation $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ is defined by $\mathrm{f}(\mathrm{x})=\mathrm{x}+2$, where $\mathrm{A}=\{-1,0,1\}$ and $\mathrm{B}=\{1,2,3\}$, then $\mathrm{f}$ is (1) only one-one function. (2) only onto function. (3) bijective. (4) None of these

In this problem of relations and functions we have given that A and B are two sets. Yeah, we have to show their the council which is from a cross B two, be across a such a day function, F A B is equal to be, It is by objective, so a function is said to be objective and then if it is 11 and onto concerned. So first we have to check for on two fronts 11 function or we can say interactivity. So first, the step of the way, check for 11 function 11 quantum. So the answer is said to be 11 if head even and say B one which belongs to here A Crosby and say 82 and B two, which also belongs from a cross big such that the function here here F off even and we won is equals two F of a two and B two. And this implies that everyone is equal to 82 beaver is equal to be too. If this condition is satisfied, we say that the sponsor is 11 So from here, F F A N B one is equal to say be even and even and F of it'll be too is B two and a two. So any order pair is said to be equal if B one is equal to be two and a one is equal to a two since this condition is satisfied. So we can say that the function is 11 and now we have to check for onto johnson. So here we are taking for onto function. So step two. Mhm. Check for check four subjectivity or onto once. Um Mhm. So let's be and with the element of be close. So this is here B and which belongs to be across A then head, element of which belongs to the given set A an element or B. Which belongs to the given said B. And this implies that here baby A. And we would be belongings from across B. So this will be from Crosby for all values of B. And A. So we say that for all values of the order will be and A. Which belongs to the big cross trade did exist. So there exist ordered pair. The ordered pair would be A. And B. A. And B. Which belongs to air Crosby. So that means every pair would have its image. Or we can say extremity in could've been. So that's why we say that the function F. Is here on two since the fence anyone went on to. So we can say that hence funds managed by objective. Hence S. Is by objective. So this is the answer.

We need to see if these orders um pairs to find Y. As a function of X. So we're just gonna look at our X. Values. We have 25 -4 and seven so excess don't repeat. So since they don't repeat, why is a function of X. So this is a yes.

And this problem were given the seven ordered pairs. That represents a relation, and what we want to do first is determined whether this relation represents a function well, if it's a function that means every X value will be assigned to exactly one. Why value? So let's take a look. Well, each X value is assigned to only one y value, and negative, too, is only assigns a seven. The negative one is only assigned to Tek. Zero is only assigned the 13 and the one is only assigned to 6 60 Therefore, this relation is a function Now. Our directions tell us if it's a function to determine the domain in the range. So let's start with the domain. Well, though domain represents the first components for each of our order pairs. So in that case, it would be negative too negative 10 and positive one. So our domain is the set off. Negative too negative. 10 and one. Now we need to find the range. Well, the range represents the second component each pair, So that will be 7 10 13 and 60. So our range will be the set off. 7 10 13 and 16

We need to determine the ordered pairs to find Y as a function of X. So if we look at our X values, none of them repeat, so exes don't repeat. Okay, so since they don't repeat, this is yes.


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