Question

If $\text{U}$ is a set of all triangles in a plane and set $\text{A}$ is the set of triangles with atleast one angle different from ${60}^{\circ }$, then ${\text{A}}^{\prime }$ is a set of ______ triangles.

• A. equilateral
• B. isosceles
• C. scalene
• D. right-angled

Answer 1

The correct option is A equilateral

Given:
$\text{U}=\{x:x\text{is a triangle}\}$
$\text{A}=\{x:x\text{is a triangle and at least}$$\text{one angle of}x\text{is not equal to}{60}^{\circ }\}$

$⟹{\text{A}}^{\prime }=\{x:x\text{is a triangle and all}$$\text{the angles of}x\text{are equal to}{60}^{\circ }\}$
So, ${\text{A}}^{\prime }=\{x:x\text{is an equilateral triangle}\}$