$128\in \left\{y\right|$ the sum of all the positive factors of $y$ is $2y$$\}$.

$3\notin \left\{x|x^4-5x^3+2x^2-112x+6=0\right\}$

State which of the following statements are true and which are false. Justify your answer.

$496\notin \{y:$ the sum of all the positive factors of $y$ is $2y$}.

Given $\mathrm{L}=\{1, 2, 3, 4\}, \mathrm{M}=\{3, 4,5, 6\}$ and $\mathrm{N}=\{1, 3, 5\}$ Verify that $\mathrm{L}-(\mathrm{M}\cup \mathrm{N})=(\mathrm{L}-\mathrm{M})\cap (\mathrm{L}-\mathrm{N})$

If $\mathrm{A}$ and $\mathrm{B}$ are subsets of the universal set $\mathrm{U}$, then show that

$\mathrm{A}\subset \mathrm{A}\cup \mathrm{B}$

If $\mathrm{A}$ and $\mathrm{B}$ are subsets of the universal set $\cup$, then show that

$\mathrm{A}\subset \mathrm{B}\iff \mathrm{A}\cup \mathrm{B}=\mathrm{B}$

If $\mathrm{A}$ and $\mathrm{B}$ are subsets of the universal set $\cup$, then show that

$(\mathrm{A}\cap \mathrm{B})\subset \mathrm{A}$

Given that $\mathrm{N}=\{1, 2, 3, \dots ,100\}$. Then write the subset of $\mathrm{N}$ whose elements are even numbers.

Given that $\mathrm{N}=\{1, 2, 3, \dots ,100\}$. Then write

the subset of $\mathrm{N}$ whose element are perfect square numbers.