Answer
a) Yes, 2 is an element of that set
b) No, 2 is not an element of that set
c) Yes, 2 is an element of that set
d) No, 2 is not an element of that set
e) No, 2 is not an element of that set
f) No, 2 is not an element of that set
Work Step by Step
a) We have a set of integers greater than 1 so the set is {2,3,4,5....+infinite}. We can see that the number 2 is an element of that set.
b) If 2 is an element of that set, then 2 would be the square of an integer that we can call it I. So we would have $\sqrt (2)= I$ . $\sqrt (2)$ is not an integer, so 2 is not an element of that set.
c) 2 is the first element of the set {2,{2}}.
d) The set is {{2}, {{2}}}. 2 is a number, and the set contains 2 sets {2} and {{2}}, it does not contain the number 2.
e) The set {{2}, {2,{2}}} contains 2 elements which are 2 sets : {2} and {2,{2}}, it does not contain an element number 2.
f) The set {{{2}}} contains 1 element which is 1 set {{2}}. It does not contain an element which is a number 2.
