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 $A^{\prime}$?

Similar Questions

If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$,$A = \{2, 4, 6, 8\}$,and $B = \{2, 3, 5, 7\}$,verify that $(A \cap B)^{\prime} = A^{\prime} \cup B^{\prime}$.

Taking the set of natural numbers as the universal set,write down the complement of the following set:
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Fill in the blank to make the following a true statement:
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