Let A = R x R, R the real number system and R={((x,y),(a,b))∈A×A∣ either x< a or x = a and y > b} Then, which one of the following is true, if (x, y) (a,b))∈R and ((a,b)∈R and ((a,b),(p,q))∈R ?

Suppose that ( $((x, y), (a, b)), ((a, b), (p, q)) \in R$
then either $x < a or x = a and y > b$

and either $a < p or a = p and b > q$

$If x < a and a < p, then x < p and hence$ $((x, y), (p, q) \in R$

Same is the case when x <a and a=p and also when x=a and a<p

If x = a y>b, a= p and b>g then x = p and y>b>q

Therefore, $((x, y), (p, q)) \in R$

Let A = R x R, R the real number system and $R = {((x, y), (a, b)) \in A \times A ∣$ either x< a or x = a and y > b} Then, which one of the following is true, if (x, y) $(a, b)) \in R$ and $((a, b) \in R$ and $((a, b), (p, q)) \in R$ ?