Let

be a commutative Noetherian ring and

be an ideal of

. Then,

has the strong persistence property if

for all

. Also, we say that

has the
symbolic strong persistence property if

for all

, where

denotes the

-th
symbolic power of

. In this paper, by using some monomial
operations, such as expansion, weighting, monomial multiple,
monomial localization, and contraction, we introduce several
methods for constructing new monomial ideals which have the
symbolic strong persistence property based on the monomial ideals
which have the symbolic strong persistence property. We also probe
the strong persistence property of the cover ideal of the union of
two finite simple graphs.