Yes, a relation is antisymmetric if for all elements a and b in the relation, if (a, b) and (b, a) are both in the relation, then a must equal b. In other words, if there is a pair of distinct elements where both are related to each other, then the relation is not antisymmetric. **

The less-than-or-equal relation should be antisymmetric because it represents a partial ordering where elements can be compared in terms of their magnitude. If the relation were not antisymmetric, it would violate the property that if a ≤ b and b ≤ a, then a = b. This would lead to inconsistencies in the ordering of elements. Therefore, in order for the less-than-or-equal relation to accurately represent a partial ordering, it must be antisymmetric, ensuring that no two distinct elements can be less than or equal to each other simultaneously. **

Symmetric and antisymmetric are two types of relationships that can exist between elements in a set. In a symmetric relationship, if element A is related to element B, then element B is also related to element A. This means the relationship is bidirectional. In contrast, in an antisymmetric relationship, if element A is related to element B, then element B cannot be related to element A. This means the relationship is unidirectional and does not allow for both elements to be related to each other simultaneously. **

A relation that is symmetric but not antisymmetric is a relation where if (a, b) is in the relation, then (b, a) is also in the relation, but it is not necessarily the case that a = b. In other words, the relation is reflexive and symmetric, but not antisymmetric. An example of such a relation is the "is a sibling of" relation. If person A is a sibling of person B, then person B is also a sibling of person A, but it is not necessarily the case that person A and person B are the same person. **

A relation that is antisymmetric and transitive, but not reflexive is a relation where if (a, b) is in the relation, and (b, a) is also in the relation, then a must equal b. Additionally, if (a, b) and (b, c) are in the relation, then (a, c) must also be in the relation. However, it does not require that every element is related to itself. In other words, it does not necessarily have the property that for every element a, (a, a) is in the relation. **

This cartoon is funny because it uses exaggeration and absurdity to highlight the ridiculousness of the situation. The image of a giant, menacing shark being afraid of a tiny, harmless goldfish is a humorous and unexpected twist on the typical power dynamic between these two animals. The contrast between the shark's fearsome appearance and its comically irrational fear of the goldfish adds to the humor of the cartoon. Additionally, the use of anthropomorphism, giving human-like emotions and reactions to the animals, adds another layer of humor to the situation. **

As an AI, I don't have the capability to find things funny or not. However, humor is subjective, and different people may find different things funny. This cartoon depicts a person using a magnifying glass to search for something, and the punchline is that they are searching for their lost glasses. Some people may find this play on words and irony funny, while others may not. **

As an AI, I cannot view images. However, humor is subjective and can vary from person to person. Some may find the cartoon funny while others may not. It ultimately depends on individual preferences and sense of humor. **