Match the following intervals in Column I with the sets in Column II and choose the correct option from the codes given below. Column I Column II A (-3,0) 1 x: x ∈ R, 6

Question

Match the following intervals in Column I with the sets in Column II and choose the correct option from the codes given below. Column I Column II A (-3,0) 1 x: x ∈ R, 6 < x ≤ 12 B [6,12] 2 x: x ∈ R,-23 ≤ x < 5 C (6,12] 3 x: x ∈ R,-3 < x < 0 D [-23,5) 4 x: x ∈ R, 6 ≤ x ≤ 12  (A) A - (1), B -(2), C -(3), D -(4) (B) A - (3), B -(4), C -(1), D -(2) (C) A - (4), B -(1), C -(2), D -(3) (D) A - (2), B -(3), C -(4), D -(1)

Tardigrade Admin · Accepted Answer

The interval (-3,0) is open at both the ends. So, it can be represent in set-builder form as x: x ∈ R,-3 < x < 0 . The interval [6,12] is closed at both end. So, it can be represent as x: x ∈ R, 6 ≤ x ≤ 12 . Similarly, we can represent other intervals.

Column I		Column II
A	$(- 3, 0)$	1	${x : x \in R, 6 < x \leq 12}$
B	$[6, 12]$	2	${x : x \in R, - 23 \leq x < 5}$
C	$(6, 12]$	3	${x : x \in R, - 3 < x < 0}$
D	$[- 23, 5)$	4	${x : x \in R, 6 \leq x \leq 12}$

Q. Match the following intervals in Column I with the sets in Column II and choose the correct option from the codes given below. Column I Column II A (−3,0) 1 {x:x∈R,6<x≤12} B [6,12] 2 {x:x∈R,−23≤x<5} C (6,12] 3 {x:x∈R,−3<x<0} D [−23,5) 4 {x:x∈R,6≤x≤12}

A - (1), B -(2), C -(3), D -(4)

A - (3), B -(4), C -(1), D -(2)

A - (4), B -(1), C -(2), D -(3)

A - (2), B -(3), C -(4), D -(1)

The interval (−3,0) is open at both the ends. So, it can be represent in set-builder form as {x:x∈R,−3<x<0}. The interval [6,12] is closed at both end. So, it can be represent as {x:x∈R,6≤x≤12}. Similarly, we can represent other intervals.

The interval $(- 3, 0)$ is open at both the ends. So, it can be represent in set-builder form as ${x : x \in R, - 3 < x < 0}$ .
The interval $[6, 12]$ is closed at both end. So, it can be represent as ${x : x \in R, 6 \leq x \leq 12}$ .
Similarly, we can represent other intervals.