decide which of the following represent true statements about the nature of set. for any that are false, provide a specific example where the statement in question does not hold.
(a) if a1 ⊇ a2 ⊇ a3 ⊇ a4 are all sets containing an infinite number of elements, then the intersection n-1 an is infinite as well.

If the intersection is finite the statement  is true, but if the intersection is infinite the statement is false.

Step-by-step explanation:

From the statement of the problem I am not sure if the intersection is finite or infinite. Then, I will study both cases.

Let us consider first the finite case: . Because the condition A1 ⊇ A2 ⊇ A3 ⊇ A4 ... we can deduce that the set is a subset of each set with . Thus,

.

Therefore, as is infinite, the intersection is infinite.

Now, if we consider the infinite intersection, i.e. the reasoning is slightly different. Take the sets

(this is, the open interval between 0 and .)

Notice that (0,1) ⊇ (0,1/2) ⊇ (0, 1/3) ⊇(0,1/4) ⊇...So, the hypothesis of the problem are fulfilled. But,

In order to prove the above statement, choose a real number between 0 and 1. Notice that, no matter how small is, there is a natural number such that . Then, the number is not in any interval with . Therefore, is not in the set [tex]\cap_{k=1}^{\infty}(0,1/k)[\tex].

there has been genes found in the x chromosome of males that have been linked to [homo/hetero]sexuality. in addition to the reign of the x chromosome, a section of chromosome 8 has also been link to, "alot of ppl are so " these facts were proven true after a 2014 study of a gay male and his strait brother. according to newscientist.com,"chromosome 14 and is mainly active in the thyroid, but also the brain. called tshr, it makes a type of receptor protein that recognises and binds to a hormone that stimulates the thyroid. in this way, the gene plays an important role in controlling thyroid function. the fact that tshr seems to be involved in sexual orientation fits with evidence that thyroid function seems to be linked to sexuality."

in conclusion, "ppl are so gay" due to their genetics.

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph