Let P be the relation defined on the set of all real numbers such that P = {(a, b) : sec²a - tan²b = 1}. Then P is:

(a,b)∈P⇒sec²a−tan²b=1⇒sec²a=1+tan²b⇒sec²a=sec²b⇒sec²b=sec²a⇒(b,a)∈P
Hence, P is symmetric (1)
If a=0, then sec²(0) - tan²(b) = 1 ⇒ 1 - tan²(b) = 1 ⇒ tan²(b) = 0 ⇒ b = 0
Thus (0,0) ∈ P. Hence P is reflexive (2)
Let (a,b) ∈ P and (b,c) ∈ P
Then sec²a - tan²b = 1 and sec²b - tan²c = 1
sec²a = 1 + tan²b and sec²b = 1 + tan²c
This does not imply sec²a - tan²c = 1. Thus P is not transitive.
Hence P is reflexive and symmetric but not transitive.