Decide if a relation on numbers is reflexive, symmetric or transitive

1. A.
   symmetric but neither reflexive nor transitive
2. B.
   reflexive but neither symmetric nor transitive
3. C.
   reflexive and symmetric, but not transitive
4. D.
   an equivalence relation

Tap an option to check your answer.

1. A.
   $(x,y) \in R \Leftrightarrow 0 < |x| - |y| \leq 1$ is neither transitive nor symmetric.
2. B.
   $(x,y) \in R \Leftrightarrow 0 < |x - y| \leq 1$ is symmetric and transitive.
3. C.
   $(x,y) \in R \Leftrightarrow |x| - |y| \leq 1$ is reflexive but not symmetric.
4. D.
   $(x,y) \in R \Leftrightarrow |x - y| \leq 1$ is reflexive and symmetric.

Tap an option to check your answer.

1. A.
   Both $R_{1}$ and $R_{2}$ are equivalence relations
2. B.
   Neither $R_{1}$ nor $R_{2}$ is an equivalence relation
3. C.
   $R_{1}$ is an equivalence relation but $R_{2}$ is not
4. D.
   $R_{2}$ is an equivalence relation but $R_{1}$ is no

Tap an option to check your answer.

1. A.
   $R_{1}$ is an equivalence relation but not $R_{2}$
2. B.
   $R_{2}$ is an equivalence relation but not $R_{1}$
3. C.
   both $R_{1}$ and $R_{2}$ are equivalence relations
4. D.
   neither $R_{1}$ nor $R_{2}$ is an equivalence relation

Tap an option to check your answer.

1. A.
   $\alpha = 14$
2. B.
   $\alpha$ is a multiple of 4
3. C.
   4 is the remainder when $\alpha$ is divided by 10
4. D.
   4 is the remainder when $\alpha$ is divided by 7

Tap an option to check your answer.

1. A.
   reflexive but not symmetric
2. B.
   transitive but not reflexive
3. C.
   symmetric but not transitive
4. D.
   neither symmetric nor transitive

Tap an option to check your answer.

1. A.
   an equivalence relation
2. B.
   transitive but not symmetric
3. C.
   not reflexive
4. D.
   symmetric but not transitive

Tap an option to check your answer.

1. A.
   neither $S$ nor $T$ is transitive
2. B.
   $S$ is transitive but $T$ is not
3. C.
   $T$ is symmetric but $S$ is not
4. D.
   both $S$ and $T$ are symmetric

Tap an option to check your answer.

1. A.
   an equivalence relation
2. B.
   reflexive and symmetric but not transitive
3. C.
   reflexive but neither symmetric nor transitive
4. D.
   reflexive and transitive but not symmetric

Tap an option to check your answer.

1. A.
   transitive but neither symmetric nor reflexive
2. B.
   reflexive but neither symmetric nor transitive
3. C.
   an equivalence relation
4. D.
   symmetric but neither reflexive nor transitive

Tap an option to check your answer.

1. A.
   reflexive and transitive but not symmetric
2. B.
   reflexive and symmetric but not transitive
3. C.
   an equivalence relation
4. D.
   symmetric and transitive but not reflexive

Tap an option to check your answer.

1. A.
   an equivalence relation
2. B.
   both reflexive and transitive but not symmetric
3. C.
   both reflexive and symmetric but not transitive
4. D.
   reflexive but neither symmetric not transitive

Tap an option to check your answer.

1. A.
   Both Statement I and Statement II are correct
2. B.
   Statement I is incorrect but Statement II is correct
3. C.
   Statement I is correct but Statement II is incorrect
4. D.
   Both Statement I and Statement II are incorrect

Tap an option to check your answer.