For each of the sets below, determine whether {2} is an element of that set. a) {x∈R ∣x is an integer greater than 1} b) {x∈R ∣ x is the square of an integer} c) {2,{2}} d) {{2},{{2}}} e) {{2},{2,{2}}} f) {{{2}}}

Question

For each of the sets below, determine whether {2} is an element of that set.  a) {x∈R ∣x is an integer greater than 1} b) {x∈R ∣ x is the square of an integer}  c) {2,{2}}  d) {{2},{{2}}}  e) {{2},{2,{2}}}  f) {{{2}}}

hosentak · Accepted Answer

(a) The set thus contains all elements greatr than 1. 2 is an integer greater than 1, thus 2 is an element of the set.  (b) The set thus contains all squares of integers. 2 is not the square of an integer, thus 2 is NOT an element of the set.  (c) The set contains the integer 2 and a subset {2} that contains the integer 2. 2 is the irst element mentioned in the set, thus 2 is an element of the set.  (d) The set contains the subset {2} and the subset {{2}} (subset containing a subset). The set contains only subsets, while 2 is not subset an thus 2 is not an element of the set.  (e) The set contains the subset {2} and the subset {2,{2}}. The set contains only subsets, while 2 is not a subset and thus 2 is not an element of the set.  (f) The set contains the subset {{2}} (subset containing a subset). The set contains only subsets, while 2 is not a subset and thus 2 is not an element of the set.

Accepted Answer

a) No   b)no   c)yes   d) yes   e) yes   f) yes

user_27qwe · Accepted Answer

Result:- {2} is not an element of the sets in parts (a), (b), (d), (e), and (f).- {2} is an element of the set in part (c).Solution:a) {x∈ℝ|x&amp;nbsp;is&amp;nbsp;an&amp;nbsp;integer&amp;nbsp;greater&amp;nbsp;than&amp;nbsp;1}In this set, we are considering real numbers that are integers greater than 1. Since {2} is not a real number but rather a set containing the element 2, it is not an element of this set. Therefore, {2} is not an element of this set.b) {x∈ℝ|x&amp;nbsp;is&amp;nbsp;the&amp;nbsp;square&amp;nbsp;of&amp;nbsp;an&amp;nbsp;integer}This set includes real numbers that are perfect squares of integers. Since 2 is not a perfect square of any integer, {2} is not an element of this set.c) {2,{2}}In this set, we have two elements: 2 and the set {2}. {2} is one of the elements in this set, so {2} is an element of this set.d) {{2},{{2}}}This set contains two elements: the set {2} and the set {{2}}. {2} is not an element of this set since it is a set itself, not a single element.e) {{2},{2,{2}}}This set has two elements: the set {2} and the set {2, {2}}. {2} is not an element of this set since it is a set itself, not a single element.f) {{{2}}}This set has a single element: the set {{2}}. {2} is not an element of this set since it is a set itself, not a single element.

karton · Accepted Answer

a) Set: A={x∈ℝ|x&amp;nbsp;is&amp;nbsp;an&amp;nbsp;integer&amp;nbsp;greater&amp;nbsp;than&amp;nbsp;1}The element 2 is not an element of this set. Therefore, {2} is not an element of set A.b) Set: B={x∈ℝ|x&amp;nbsp;is&amp;nbsp;the&amp;nbsp;square&amp;nbsp;of&amp;nbsp;an&amp;nbsp;integer}The element 2 is not a perfect square of any integer. Therefore, {2} is not an element of set B.c) Set: C={2,{2}}The element 2 is an element of this set. Therefore, {2} is an element of set C.d) Set: D={{2},{{2}}}The element 2 is not an element of this set. Therefore, {2} is not an element of set D.e) Set: E={{2},{2,{2}}}The element 2 is an element of this set. Therefore, {2} is an element of set E.f) Set: F={{{2}}}The element 2 is not an element of this set. Therefore, {2} is not an element of set F.

For each of the sets below, determine whether {2} is

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