# Prove or disprove the following proposition

$$L_1^*∪L_2^*⊆(L_1∪L_2)^*$$

I actually disproved the opposite proposition $$[(L_1∪L_2)^*⊆L_1^*∪L_2^*]$$ and my intuition tells me that this is actually true… I tried to show that the combinations of words in the right group $$[(L_1∪L_2)^*]$$ obviously contain all the words from the left group $$[L_1^*∪L_2^*]$$ and it’s also very plain to see, but I have no idea how to formalize it.

Any idea how to formally prove it? Thanks.