I'm wondering whether my derived and logic are correct or not pleasr help me check it.

Income effect , Substitude Effect and Total for each type of good.

x is each type of good

Normal good x price increase Normal good x price decrease

Normal good y price hold Normal good y price hold

total effect: ambiguos total effect: ambiguos

Inferior good x price increase Inferior good x price decrease

Normal good y price hold Normal good y price hold

total effect: (x decrease, y increase) total effect:(x decrease, y increase)

=> SUBSTITUTION effect dominate

Giffen good x price increase Giffen good x price decrease

Normal good y price hold Normal good y price hold

total effect: (x increase, y decrease) total effect:(x decrease, y increase)

=> Income effect dominate