Question

which of the following sets are empty sets? justify your answer. 1) A = { x : x 2 = 4 and 3 x = 9 2) The set of all triangles in a plane having the sum of their three angles less than 180. ​

Answer 1

Answer:

Empty set is a set which does not contains any element.

i] Set of all even natural numbers divisible by 5

→ Not a Empty set, e.q. 10, seven natural number &

divisible by 5.

ii] Set of all even prime number

→ not a Empty set e.q. 2 is even prime number

iii] {x:x

2

−2=0 & x is rational }

→ not a Empty set, e.q. x=2 satisfy which is a

rational number.

iv] {x:x is a natural number x < 8 & x > 12 }

→ It is a empty set because if a natural number is less

than 8, then it cannot be greater than 12.

v] {x:x is a point common to any two parallel lines }

→ A empty set because there will be no common

point between two parallel lins.

So (iv) & (v) are examples of empty of empty sets.

Answer 2

1) is not an empty set

1) is not an empty set 2) is an empty set because the sum of triangle can't be less or more than 180.