Relations

Step 1: Checking reflexivity.
A relation is reflexive if for every element $x$ in the set, the pair $(x%2C%20x)$ belongs to the relation. In this case, the set is $%5C%7B1%2C%202%2C%203%2C%204%5C%7D$ . The pairs $(1%2C%201)%2C%20(2%2C%202)%2C%20(3%2C%203)%2C%20(4%2C%204)$ are all present in the relation, so the relation is reflexive.

Step 2: Checking transitivity.
A relation is transitive if whenever $(a%2C%20b)$ and $(b%2C%20c)$ are in the relation, then $(a%2C%20c)$ must also be in the relation. - We have $(1%2C%202)$ and $(2%2C%203)$ , so $(1%2C%203)$ must also be present, which it is. - We also have $(3%2C%202)$ and $(2%2C%202)$ , so $(3%2C%202)$ is present. Since all necessary pairs are present, the relation is transitive.

Step 3: Checking symmetry.
A relation is symmetric if whenever $(a%2C%20b)$ is in the relation, $(b%2C%20a)$ must also be in the relation. In this case, $(1%2C%202)$ is in the relation, but $(2%2C%201)$ is not, so the relation is not symmetric.

Step 4: Conclusion.
The relation is reflexive and transitive, but not symmetric.

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

Relations

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Chapter Questions
2 MCQs