Question

check whether {x:x^2=25 and 6x=15} is an empty set or not?justify your answer.​

Answer 1

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Answer :-

Empty set

Solution :-

Let, A = { x : x² = 25 and 6x = 15 }

Finding x when x² = 25

⇒ x² = 25

⇒ x = √25

⇒ x = ± 5

⇒ x = 5 or - 5

Finding x when 6x = 15

⇒ 6x = 15

⇒ x = 15 / 6

⇒ x = 2.5

Since, the value of x in both cases are different there is no value of x that satisfies the given rule.

So, the set A = Φ

Therefore the set { x : x² = 25 and 6x = 15 } is an empty set.

Answer 2

Answer:

Empty set

Solution :-

Let, A = { x : x² = 25 and 6x = 15 }

Finding x when x² = 25

⇒ x² = 25

⇒ x = √25

⇒ x = ± 5

⇒ x = 5 or - 5

Finding x when 6x = 15

⇒ 6x = 15

⇒ x = 15 / 6

⇒ x = 2.5

Since, the value of x in both cases are different there is no value of x that satisfies the given rule.

So, the set A = Φ

Therefore the set { x : x² = 25 and 6x = 15 } is an empty set.