Question

for interval (-1, 1) which of the following statement is true ?
(a) -1 € (-1, 1]
(b) o € (-1, 1)
(c) (-1, 1] = {-1, 1}
(d) (-1, 1] = {o}​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

For interval (-1, 1) which of the following statement is true

(a) -1 ∈ (-1, 1]

(b) 0 ∈ (-1, 1)

(c) (-1, 1] = {-1, 1}

(d) (-1, 1] = {0}

EVALUATION

CHECKING FOR OPTION (a)

Since - 1 does not belong to the interval (-1, 1]

So this option is not correct

CHECKING FOR OPTION (b)

Clearly - 1 < 0 < 1

So 0 ∈ (-1, 1)

So this option is correct

CHECKING FOR OPTION (c)

For the interval (-1, 1] we have

- 1 < x ≤ 1

So there are many points which are greater than - 1 and less than equal to 1 other than - 1 & 1 in the interval (-1, 1]

So this option is not correct

CHECKING FOR OPTION (d)

For the interval (-1, 1] we have

- 1 < x ≤ 1

So there are many points which are greater than - 1 and less than equal to 1 other than 0 in the interval (-1, 1]

So this option is not correct

FINAL ANSWER

Hence the correct option is (b) 0 ∈ (-1, 1)

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