and The main tools for the proofs of our results are following differential equation and inequalities. where and The following theorem is a generalization of Theorem 1 in [16] to impulsive delay differential equations with continuous and piecewise constant arguments. Theorem 1. ( i ) Inequality (3) has no eventually positive solution if and only if inequality (6) has no eventually positive solution. ( ii ) Inequality (4) has no eventually negative solution if and only if inequality (7) has no eventually negative solution. ( iii ) All solutions of the equation (1)-(2) are oscillatory if and only if all solutions of equation (5) are oscillatory. 4 Proof. We will prove ( i ) since the proofs of ( ii ) and ( iii ) are similar to proof C ( t ) = ∏ [ t − 1] <t$_{j}$ ≤ t (1 − b$_{j}$ ) c ( t ) , t ≥ t$_{0}$ + max { τ, 2 } . (9) B ( t ) = ∏ t − τ<t$_{j}$ ≤ t (1 − b$_{j}$ ) b ( t ) , t ≥ t$_{0}$ + max { τ, 2 } , (8) y $^{′}$( t ) + a ( t ) y ( t ) + B ( t ) y ( t − τ ) + C ( t ) y ([ t − 1]) ≥ 0 , t ≥ t$_{0}$ + max { τ, 2 } , (7) y $^{′}$( t ) + a ( t ) y ( t ) + B ( t ) y ( t − τ ) + C ( t ) y ([ t − 1]) ≤ 0 , t ≥ t$_{0}$ + max { τ, 2 } , (6) y $^{′}$( t ) + a ( t ) y ( t ) + B ( t ) y ( t − τ ) + C ( t ) y ([ t − 1]) = 0 , t ≥ t$_{0}$ + max { τ, 2 } (5) x $^{′}$( t ) + a ( t ) x ( t ) + b ( t ) x ( t − τ ) + c ( t ) x ([ t − 1]) ≥ 0 , t = t$_{i}$, t ≥ t$_{0}$ > 0 , (4) Δ x ( t$_{i}$ ) = b$_{i}$x ( t$_{i}$ ) , i = 1 , 2 , ...