Question

1. List the members of following set
I.{x:x is real number such that x²= 4}
II.{x:x is an integer such that x²=2}

Answer 1

Answer:

I. { –2 , 2 }

II. ∅

Solution:

I. {x : x is real number such that x² = 4}

Let the given set be A .

Thus,

A = {x : x is real number such that x² = 4}

Now,

Let's find the possible real values of x for which x² = 4 .

=> x² = 4

=> x = √4

=> x = ± 2 € R

Clearly , the obtained values of x ( ie; ± 2 ) are real numbers , thus elements of the given set will be (–2) and 2 .

Hence,

A = { –2 , 2 }

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II. {x : x is integer such that x² = 2}

Let the given set be B .

Thus,

B = {x : x is integer such that x² = 2}

Now,

Let's find the possible integral values of x for which x² = 2 .

=> x² = 2

=> x = ± √2 ∉ Z

Clearly,

The obtained values of x ( ie ; ± √2 ) are not integers. Thus, the given set is an empty set .

Hence,

B = ∅