A. every set has an element. b. the smallest perfect number is 28. c. is 1.5 an irrational number? d. find the popular approximation of pi. e. can you extract the root of -25?

a) False. b) False. c) No, it's Rational. d) pi=355/113 e) 5i (for Complex Set of Numbers)

Step-by-step explanation:

a) Since there is the empty set. And an axiom assures us the existence of this Set. "There is a set such no element belongs to it"

∅ has no elements.

b) A perfect number is a positive integer equals to the sum of proper divisions

The smallest is 6. Since the proper divisors of 6={3,2,1}. 6=1+2+3

28 is a perfect number, but not the smallest. It is perfect since

28 proper divisors={14,7,4,2} 28=1+2+3+4+5+6+7

c) No, An Irrational number cannot be written as a fraction a/b where "a" and "b" are integers. 1.5 is a rational one, since 3/2 =1.5

d)

=22/7 -1/791= 355/113

e)  Not for Real Numbers, since it is not defined for Real numbers. But for the set of Complex 5i

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for