Reflexive Relations

Q. Let R be the relation on the set of all real numbers defined by a R b iff $|a-b|\le 1$. Then R is

1. Symmetric only
2. Transitive only
3. Reflexive and Symmetric
4. Anti-symmetric only

Q. Assertion :If $r_{xy}$ i.e. $r(x,y)=0.25,{\sigma }_x=0.1,{\sigma }_y=4,$ then $b_{yx}=10$ Reason: $b_{yx}=r\frac{{\sigma }_y}{{\sigma }_x}$

1. Both Assertion &. Reason are individually true & Reason is correct explanation of Assertion.
2. Both Assertion & Reason are individually true but Reason is not the correct (proper) explanation of Assertion.
3. Assertion is true Reason is false.
4. Assertion is false Reason is true.

Q. Let 𝐀 = {𝟑, 𝟒, 𝟕, 𝟖} and 𝐁 = {𝟏, 𝟕, 𝟏𝟎}. Which of the following sets are relations from 𝐀 to 𝐁?
(i) 𝐑𝟏 ={(𝟑, 𝟕), (𝟒, 𝟕), (𝟕, 𝟏𝟎), (𝟖, 𝟏)}
(ii) 𝐑𝟐 = {(𝟑, 𝟏), (𝟒, 𝟏𝟐)}
(iii) 𝐑𝟑 = {(𝟑, 𝟕), (𝟒, 𝟏𝟎), (𝟕, 𝟕), (𝟕, 𝟖), (𝟖, 𝟏𝟏), (𝟖, 𝟕), (𝟖, 𝟏𝟎)}.