GATE Overflow Test Series | Discrete Mathematics | Test 1 | Question: 9

Question

Consider set $A = \{\phi, \{1,2\},4,\{3\}\}.$ Which of the following is a subset of $A?$ (Mark all the appropriate choices)

• A. $\{1,2\}$
• B. $\{\{3\}\}$
• C. $\{3\}$
• D. $\{4,3\}$

Comments

I think option A and option B both are correct, since option A is subset,also option B is subset while C, D arent elements of set A

Answer 1

$\{1,2\}$ and $\{3\}$ are the elements of the set $A.$.

$\{\{3\}\}$ is a subset of $A,$ and so is the correct answer.   

$\{4,3\}$ is neither a subset nor an element.

Answer 2

$A = \{\phi, \{1,2\},4,\{3\}\}$

The set $A$ is a subset of $B$ if every element that is in $A$ is also in $B.$ This is denoted by $A \subseteq B.$

• $\phi \subseteq A$
• $\{\phi\} \subseteq A$
• $\{\{1,2\}\}\subseteq A$
• $\{4\} \subseteq A$
• $\{\{3\}\}\subseteq A$
• $A\subseteq A$

Each object in a set is called an element of the set. The mathematical notation for "is an element of" is $\in.$ For example, to denote that $5$ is an element of the set  $A$ of positive even integers, one writes $5 \in A$. To indicate that an element, $7,$ is not in the set $A,$ write $7 \notin A.$

• $\phi \in A $
• $\{1,2\}\in A$
• $4 \in A$
• $\{3\} \in A$

So, the correct answer is $(B).$