If the second array is a subset of the first array of the same order and starting at position 1, you can use this array formula to test equivalence:
=IFERROR(IF({1,2,3,4,5}={1,2},TRUE),FALSE)
For nonequivalence, simply replace FALSE and TRUE
=IFERROR(IF({1,2,3,4,5}={1,2},FALSE),TRUE)
Then you can use this in other formulas just like an array:

However, if the arrays are out of order, as in this example:
{1,2,3,4,5},{1,4,5}
Then you should use MATCH . However, all you need to do is surround the match with ISNUMBER as follows:
Equivalence:
=ISNUMBER(MATCH({1,2,3,4,5},{1,4,5},0))
Inequivalence:
=NOT(ISNUMBER(MATCH({1,2,3,4,5},{1,4,5},0)))
Remember that all array formulas are entered using ctrl + shift + enter