ISI2016-MMA-13

Question

Which one of the following statements is correct regarding the elements and subsets of the set $\{1, 2, \{1, 2, 3\}\}$?

• A. $\{1, 2\} \in \{1, 2, \{1, 2, 3\} \}$
• B. $\{1, 2\} \subseteq \{1, 2, \{1, 2, 3\} \}$
• C. $\{1, 2, 3\} \subseteq \{1, 2, \{1, 2, 3\} \}$
• D. $3 \in \{1, 2, \{1, 2, 3\} \}$

Answer 1

Anser:B

A.  {1,2}  is subset of {1,2,{1,2,3}}

B : {1,2}  is subset of {1,2,{1,2,3}}

C: {1,2,3}  is element in  set  {1,2,{1,2,3}}

D: 3  neither element nor subset of {1,2,{1,2,3}}

Answer 2

Concept recap

 {1,2} ∈ {1,2} is false as in case of ∈ {1,2} is taken as set and entire unit should be present.  {1,2} $∈$ {1,2, {1.2} } would be true.

{1.2} ⊆  {1,2,3} is true as here it will be checked individually if 1 and 2 are present.

Coming to the question

A.  {1,2}  ∈ {1,2,{1,2,3}} is false as {1.2} as a whole (set) isn't there in it.

B. {1,2}  ⊆ {1,2,{1,2,3}} is true as both 1 and 2 are present in it.

C. {1,2,3} ⊆ {1,2,{1,2,3}} is false as 3 doesn't belong to it.

D. 3  { 1,2,{1,2,3}} s false as 3 doesn't belong to it.

So B is correct.