Question

Which of the following sets are empty sets? Justify your answer.
(i) A = {x : x² = 4 and 3x = 9}.
(ii) The set of all triangles in a plane having the sum of their three angles less than 180.

Answer 1

Step-by-step explanation:

1. Is not a empty set.
2. Is a empty set because sum of all triangle can't be less are more than 180degres

Answer 2

Answer:

• A = {x : x² = 4 and 3x = 9} is a non-empty set.

• The set of all triangles in a plane having the sum of their three angles less than 180° is an empty set.

Step-by-step explanation:

    Given set

• A = {x : x² = 4 and 3x = 9}

   By the above condition in the set

                 x² = 4

                 x = √4

                 x = 2

      then 3x = 3(2) = 9

         Since, the condition satisfies and there exist a value for x such that

     for x = 2 , 3x = 9.

     So, the given set  A = {x : x² = 4 and 3x = 9} is a non - empty set.

• Given,

        The set of all triangles in a plane having the sum of their

         three angles less than 180°.  

        By Angle Sum property, we have

        Sum of all the three internal angles is always equal to 180°.

        So, there is no such a set of all triangles which satisfies that sum

         of all their three angles is less than 180°.

         Hence, the second set is an empty set.

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