1. Which of the following relations on {0, 1, 2, 3, 4} are reflexive? Irreflexive? Neither? 2. Let R ⊆ A × A and T ⊆ A × A be relations. Prove or disprove the following:1. R is reflexive if and only if R−1 is reflexive.2. if R and T are both reflexive, then R ◦ T is reflexive.3. if R ◦ T is reflexive, then R and T are both reflexive.4. R is irreflexive if and only if R−1 is irreflexive.5. if R and T are both irreflexive, then R ◦ T is irreflexive.

1. Which of the following relations on {0, 1, 2, 3, 4} are reflexive? Irreflexive? Neither? 2. Let R ⊆ A × A and T ⊆ A × A be relations. Prove or disprove the following: 1. R is...

1. Which of the following relations on {0, 1, 2, 3, 4} are reflexive? Irreflexive? Neither?

2. Let R ⊆ A × A and T ⊆ A × A be relations. Prove or disprove the following:

1. R is reflexive if and only if R⁻¹
is reflexive.

2. if R and T are both reflexive, then R ◦ T is reflexive.

3. if R ◦ T is reflexive, then R and T are both reflexive.

4. R is irreflexive if and only if R⁻¹
is irreflexive.

5. if R and T are both irreflexive, then R ◦ T is irreflexive.

May 07, 2022