The relationship 'part to whole' describes a component and the complete object it belongs to. An arc is a curved portion of the circumference of a circle, making 'circle' the correct whole.

The relationship between 'Run' and 'Race' is that a run is a primary activity performed within the context of a race. Similarly, a dance is a primary activity performed within the context of a party. This analogy identifies the activity and the event where it typically occurs, making 'Party : Dance' the most logical choice among the provided options.

The relationship in 'Satisfy: Hunger' is that of a verb acting to resolve or eliminate a specific condition or state. 'Quell' means to suppress or put an end to, and 'rebellion' is the state being suppressed, which perfectly mirrors the functional relationship of the original pair.

The relationship between the words is one of intensity, where the second term represents an extreme or heightened state of the first term. Euphoria is an intense form of joy, and similarly, depression is an intense or clinical form of melancholy, making this the correct parallel.

A mace is a ceremonial staff that serves as a symbol of majesty or authority. Similarly, a book is frequently used as a symbolic representation of knowledge. This relationship establishes a connection between an object and the abstract concept it represents, making 'Book: Knowledge' the most appropriate choice among the given alternatives.

This analogy identifies a raw material and the skilled professional who works with it to create finished products. A cobbler uses leather as their primary material to craft footwear. Similarly, a carpenter uses wood as their primary material to construct various structures or items, making 'Carpenter' the correct counterpart.

This analogy identifies the relationship between a functional fastening device and the object it secures. A clasp is the mechanism used to fasten a bracelet. Similarly, a buckle is the specific mechanism used to fasten a belt. This functional relationship makes option C the most appropriate choice.

The analogy identifies a specific anatomical feature characteristic of a particular animal. A bull is known for having horns, and a stag is known for having antlers. Thus, 'Antlers: Stag' correctly maintains the relationship of the animal and its defining head feature.

This analogy relates a subject to the typical reaction or treatment they receive from society. A hero is someone who earns or receives an accolade for their deeds, whereas a laughingstock is someone who is subjected to ridicule by others.

The relationship between 'Religion' and 'Ritual' is that a ritual is a practical expression or manifestation of a religious belief. Similarly, 'Belief' and 'Practice' share a parallel relationship, where a practice serves as the external application or manifestation of an internal belief system.