Questions & Answers

Question

Answers

1) $\{ a\} $

2) $\{ a,b\} $

3) $\{ 1,2,3\} $

4) $\emptyset $

Answer
Verified

Here we going to write subsets, for that, we use some rules,

The first rule is, “Empty set is a subset of every set”.

The second rule is, “The set itself is a subset of the set”.

1) \[\{ a\} \]

We can take \[A = \{ a\} \]

As we say the first rule, “empty set is a subset of every set”

That is

\[\emptyset \subseteq A\]

As we say the second rule, “the set itself is a subset for set”

\[\{ a\} \subseteq A\]

Hence \[\emptyset ,\{ a\} \] are the only subsets of \[A = \{ a\} \]

2) \[\{ a,b\} \]

We can take \[A = \{ a,b\} \]

As we say the first rule

\[\emptyset \subseteq A\]

The second rule,

\[\{ a,b\} \subseteq A\]

Also we can write,

\[\{ a\} \subseteq A\]

\[\{ b\} \subseteq A\]

Hence \[\emptyset ,\{ a,b\} ,\{ a\} ,\{ b\} \] are the subsets of set \[A = \{ a,b\} \]

3) \[\{ 1,2,3\} \]

We can take \[A = \{ 1,2,3\} \]

By the first rule,

\[\emptyset \subseteq A\]

In the second rule,

\[\{ 1,2,3\} \subseteq A\]

Then,

\[\{ 1\} \subseteq A\]

\[\{ 2\} \subseteq A\]

\[\{ 3\} \subseteq A\]

Hence \[\emptyset ,\{ 1,2,3\} ,\{ 1\} ,\{ 2\} ,\{ 3\} \] are the subsets of set \[A = \{ 1,2,3\} \]

4) \[\emptyset \]

It is different from other sets, \[\emptyset \] is the empty set.

Empty set has no elements inside the set.

Therefore it has no subsets.

Hence the set \[\emptyset \] has no subsets.