Question

If $A=\left\{\text{Isosceles triangles}\right\}$ and $B=\left\{\text{Isosceles right-angled triangles}\right\},$ then which of the following statements is/are true?

• A. $A\subseteq B$
• B. $B\subseteq A$
• C. $A\cup B=A$
• D. $A\cap B=B$

Answer 1

Answer: (B), (C), (D)

The correct options are
B

$B\subseteq A$

C

$A\cup B=A$

D

$A\cap B=B$

Given that
$A=\left\{\text{Isosceles triangles}\right\}$ and $B=\left\{\text{Isosceles right-angled triangles}\right\}.$

Clearly, all isosceles right-angle triangles are isosceles, but not all isosceles triangles are right-angled.

$\Rightarrow B\subseteq A$
$\Rightarrow A\cup B=A$ and $A\cap B=B$
(Properties of intersection and union of sets)