Question

Given, A = $\left\{Triangles\right\}$,B=$\left\{Isoscelestriangles\right\}$,C=$\left\{Equilateraltriangles\right\}$. State whether the following are true or false. Give reasons. (i)$A\subset B$ (ii)$B\subseteq A$ (iii) $C\subseteq B$ (iv)$B\subseteq A$ (v)$C\subset A$ (vi)$C\subseteq B\subseteq A$

Answer 1

(i) Since each triangle is not isosceles. $\therefore$ $A\subset B...........False$ (ii)$B\subseteq A$.....True $\because$ Isosceles $△$ is one of the triangles. (iii) Since each equilateral triangle is isosceles also, $\therefore$ $C\subseteq B$.....True. (iv)$B\subseteq A$.......True. $\because$ isosceles $△$ is one of the triangles. (v)$C\subset A$.......True $\because$ Equilateral $△$ is one of the triangles. (vi)$C\subseteq B\subseteq A$........True $\because$ Each equilateral triangle is isosceles also and each isosceles $△$ is a form of triangles.