Let U be the set of all triangles in a plane. | vedclass

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Question

(A) The universal set $U$ consists of all triangles in a plane.Set $A$ consists of all triangles that have at least one angle not equal to $60^{\circ}

Vedclass · Accepted Answer

The set of all equilateral triangles.

Vedclass · Answer

(A) The universal set $U$ consists of all triangles in a plane.Set $A$ consists of all triangles that have at least one angle not equal to $60^{\circ}$.The complement $A^{\prime}$ consists of all triangles in $U$ that are not in $A$.This means $A^{\prime}$ contains all triangles where every angle is equal to $60^{\circ}$.Since the sum of angles in a triangle is $180^{\circ}$,if every angle is $60^{\circ}$,the triangle must be equilateral.Therefore,$A^{\prime}$ is the set of all equilateral triangles.

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 $A^{\prime}$?

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