Answer:
It is NOT TRUE
Step-by-step explanation:
ꓯyꓱxP(x,y)
means that for each value of y there exist x such that P(x,y) is true
whereas
ꓱxꓯyP(x,y)
means that there exists x such that for each value y, P(x,y) is true.
In the second case, the same x must work for every element y.
Counter-example
Consider
P(x,y) the following proposition
x-y = 0, for x, y integers.
Given an integer y, there is another integer x (namely, x=-y) such that
x-y = 0
so, ꓯyꓱxP(x,y) is TRUE
If ꓱxꓯyP(x,y) were TRUE, then would exist a single unique value of x such that P(x,y) is TRUE for every integer y.
Then P(x,1) and P(x,2) would be both TRUE and
x-1 = 0
x-2 = 0
and we conclude 1=2, which is a contradiction.
So ꓱxꓯyP(x,y) is NOT TRUE (FALSE)
