Question

Given, $A=\left\{Quadrilaterals\right\},B=\left\{Rectangles\right\},C=\left\{Squares\right\}D=\left\{Rhombuses\right\}$. State, giving reasons, whether the following are true or false. (i)$B\subset C\left(ii\right)D\subset B\left(iii\right)C\subseteq B\subseteq A\left(iv\right)D\subset A\left(v\right)B\supseteq C\left(vi\right)A\supseteq B\supseteq D$

Answer 1

$A=\left\{Quadrilaterals\right\},B=\left\{Rectangles\right\},C=\left\{Square\right\}D=\left\{Rhombuses\right\}$ (i)$B\subset C$..... is a False. $\because$ Rectangle is not a square also. (ii)$D\subset B$..... is a False. $\because$ Rhombus is not a rectangle also. (iii)$C\subseteq B\subseteq A$....True. $\because$ Every Square is a rectangle also and every rectangle is a quadrilateral also. (iv)$D\subset A$.....True. $\because$ Rhombus is one of the quadrilaterals. (v)$B\supseteq C$....True. $\because$ Square is rectangle also. (vi)$A\supseteq B\supseteq D$ $\because$ Rhombus is not a rectangle also.