Question

Let $U$ be the set of all triangles in a plane. If $A$ is the set of all triangles with at least one angle different from ${60}^{\circ }$, what is $A^{\prime }$ ?

• A. $A^{\prime }$ is the set of all isosceles triangles.
• B. $A^{\prime }$ is the set of all right-angled triangles.
• C. $A^{\prime }$ is the set of all acute angle triangles.
• D. $A^{\prime }$ is the set of all equilateral triangles.

Answer 1

The correct option is D $A^{\prime }$ is the set of all equilateral triangles.

The universal set $\left(U\right)$ includes every possible triangle.
Set $A$ includes the triangles with at least one angle different from ${60}^{\circ }$. So, set $A^{\prime }$ includes those triangles with no angle different from ${60}^{\circ }$.
Hence, $A^{\prime }$ is the set of all equilateral triangles.