Transitive Relations

Q.

If the relation is defined on $R$ by $(x,y)\in S\iff xy\ge 0$, then $S$ is

1. an equivalence relation

2. symmetric only

3. reflexive only

4. transitive only

Q. Let A = {a, b, c} and the relation R be defined on A as follows:
R = {(a, a), (b, c), (a, b)}.
Then, the minimum number of ordered pairs to be added in R to make it reflexive and transitive, is

Q. 7. Let a, b, c be positive real numbers such that a/1+b + b/1+c + c/1+a = 1 Prove that abc is smaller than or equal to

Q.

Let R be a relation on the set N be defined by $\left\{\right(x,y)|x,y|N,2x+y=41\}$. Then R is

1. Reflexive

2. Symmetric

3. Transitive

4. None of these

Q. The two polar coordinates are $(44,{150}^o)$ and $(44,{30}^o)$. Find the distance between them.

1. $44\sqrt{2}$
2. $22\sqrt{3}$
3. $51\sqrt{3}$
4. $44\sqrt{3}$