Practicing Success
If R and R' are symmetric relations (not disjoint) on a set A, then the relation R ∩ R' is |
reflexive symmetric transitive none of these |
symmetric |
Since R ∩ R' are not disjoint, there is at least one ordered pair, say, (a, b) in R ∩ R'. but (a, b) ∈ R ∩ R' ⇒ (a, b) ∈ R and (a, b) ∈ R' since R and R' are symmetric relations, we get (b, a) ∈ R and (b, a) ∈ R' and consequently (b, a) ∈ R ∩ R' similarly if any other ordered pair (c, d) ∈ R ∩ R', then we must also have, (d, c) ∈ R ∩ R' hence R ∩ R' is symmetric. Hence (2) is the correct answer. |