What universal set will you write for the following set in a plane:

The set of isosceles triangles

What universal set will you write for the following set in a plane:

The set of equilateral triangles

Given the sets $A=\left\{2, 4, 6\right\}, B=\left\{1, 3, 4, 5\right\}, C=\left\{0, 1, 3, 4, 6, 8\right\}$; which of the following sets may be taken as universal set for all the three sets $A, B$ and $C$:

Determine whether the statement given below is true or false. If it is true, prove it. If it is false, give an example:

If $x\in A \mathrm{and} \mathrm{A}\in \mathrm{B}$, then $x\in B$.

Determine whether the statement given below is true or false. If it is true, prove it. If it is false, give an example:

If $\mathrm{A}\subset \mathrm{B} \mathrm{and} \mathrm{B}\in \mathrm{C},$ then $A\in C$.

Determine whether the statement given below is true or false. If it is true, prove it. If it is false, give an example:

If $\mathrm{A}\subset \mathrm{B} \mathrm{and} \mathrm{B}\subset \mathrm{C},$ then $A\subset C$.

Determine whether the statement given below is true or false. If it is true, prove it. If it is false, give an example:

If $\mathrm{A}\not\subset \mathrm{B} \mathrm{and} \mathrm{B}\not\subset \mathrm{C},$ then $A\not\subset C$.

Determine whether the statement given below is true or false. If it is true, prove it. If it is false, give an example:

If $\mathrm{x}\in \mathrm{A} \mathrm{and} A\not\subset B,$ then $x\in B$.

Determine whether the statement given below is true or false. If it is true, prove it. If it is false, give an example:

If $\mathrm{A}\subset \mathrm{B} \mathrm{and} x\notin B,$ then $x\notin A$.