Question

Which of the following is/are singleton sets?

• A. $A=\{x:x\text{is H.C.F. of}12\text{and}18\}$
• B. $B=\{x:x\text{is a common prime factor of}16\text{and}27\}$
• C. $C=\{x:x\text{is a prime factor of}35\}$
• D. $D=\{x:x\text{is L.C.M. of}6\text{and}11\}$

Answer 1

Answer: (A), (D)

$D=\{x:x\text{is L.C.M. of}6\text{and}11\}$

$A=\{x:x\text{is H.C.F. of}12\text{and}18\}$
H.C.F. of $12$ and $18$ is $6$
$A=\left\{6\right\}$
Set $A$ is a singleton set

$B=\{x:x\text{is a common prime factor of}16\text{and}27\}$
$1$ is the only common factor of $16$ and $27$, which is not prime
So $B=\varphi$
Set $B$ is not a singleton set

$C=\{x:x\text{is a prime factor of}35\}$
Prime factors of $35$ is $5,7$
$C=\{5,7\}$
Set $C$ is not a singleton set

$D=\{x:x\text{is L.C.M. of}6\text{and}11\}$
L.C.M. of $6$ and $11$ is $66$
$D=\left\{66\right\}$
Set $D$ is a singleton set