Let:
S1 = X is red
S2 = Y is not red
S3 = Z is not blue

if S1 is TRUE, then S2 will also be TRUE - this cannot be, so S1 is FALSE
Now if S2 is TRUE, then Z is Red => S3 is TRUE - this also cannot be, S2 is FALSE
This leaves S3 is TRUE
=> Z is Red or White
Since S2 is FALSE Y is Red => Z is White => X is Blue

Let:

S1 = X is red

S2 = Y is not red

S3 = Z is not blue

if S1 is TRUE, then S2 will also be TRUE - this cannot be, so S1 is FALSE

Now if S2 is TRUE, then Z is Red => S3 is TRUE - this also cannot be, S2 is FALSE

This leaves S3 is TRUE

=> Z is Red or White

Since S2 is FALSE Y is Red => Z is White => X is Blue

Therefore:

X = Blue

Y = Red

Z = White