5. For each set below, say whether it is finite,countably infinite, or uncountable. Justify your answer in eachcase, giving a brief reason rather than an actualproof.
a. The points along the circumference of a unitcircle.
(Uncountable because across the unit circle because points areone-to-one correspondence to real numbers) so they areuncountable
b. The carbon atoms in a single page of thetextbook.
("Finite", since we are able to count the number of atoms in asingle page of textbook)(The single page is the limit and itcontains a number of carbon atom elements)
c. The different angles that could be formed when twolines intersect (e.g. 30 degrees, 45 degrees, 359.89 degrees,etc….)
("uncountable" because, the different angles that can be madewould be in radial from 0-2pi, pi is an example of irrational angleand cannot be counted in the set.
d. All irrationals which are exact square roots of anatural number.
("countably infinite", there are infinite perfect squares as xapproaches infinity, so there are infinite exact square roots for anatural number, which is one to one correspondence and is ontotherefore is countable
e. All irrationals of the form a+sqrt(b) where a and bare rational numbers.
(im unsure about this one but i would say "uncountable" becausenot all a+sqrt(b) will be rational, sqrt(b) would have to be rationfor it to be a countable, since irrational numbers arecountable
f. The set of all squares that can be drawn within aunit circle.
"Uncountable" it has a one to one correspondence from 0 to2pi
i wanted to crosscheck n see if this is right
