Based on the image, which of the provided options is correct?

Let's analyze the provided options based on the diagram. The diagram shows two sets, B and E, represented as closed curves. Set E is entirely contained within set B. We need to determine which of the options is correct according to this diagram.

A) (B subset E) - This means B is a subset of E, which is incorrect because E is inside B, not the other way around.

B) (3 in B) - This means 3 belongs to B. Since 3 is inside set E, and E is inside B, then 3 is inside B. This statement is true.

C) (5 otin E) - This means 5 does not belong to E. Point 5 is outside set E, so this statement is true.

D) (E otsubset B) - This means E is not a subset of B, which is false because E is clearly inside B.

E) (5 otin B) - This means 5 does not belong to B. Point 5 is inside B, so this statement is false.

F) (E subset B) - This means E is a subset of B, which is true because E is entirely contained within B.

G) (5 in E) - This means 5 belongs to E. Point 5 is outside set E, so this statement is false.

H) (7 in E) - This means 7 belongs to E. Point 7 is inside set E, so this statement is true.

The checked option in the image is H) (7 in E), which, as we determined, is true.