Are these DCFL? Why ?

Question

1) $a^{n}b^{n} \cup a^{n}b^{2n} ; n\geq 0$

2) $a^{n}cb^{n} \cup a^{n}db^{2n} ; n\geq 0$

3)$ca^{n}b^{n} \cup da^{n}b^{2n} ; n\geq 0$

Answer 1

1) It is not DCFL and it's in CFL

Reason:  given a input after reading all a's we will not deterministically know whether to pop out 'a' for single 'b' (a^nb^n)or double 'b'(a^nb^2n)

2)It is in DCFL

Reason: you can use 'c' and 'd' to deterministically decide whether it is a^nb^n or a^nb^2n after reading all a and the next ip charecter

3) it is in DCFL

Reason:  you can use 'c' and 'd' to deterministically decide whether it is a^nb^n or a^nb^2n after reading the first ip charecter(i.e,.whether the first char is c or d)

Comments

here is what I think

caⁿbⁿ  is a CFL (here we can't distinguish 'a' and 'b' deterministically ) and daⁿb²ⁿ is also a CFL(ere also we can't distinguish 'a' and 'b' deterministically )  

Both the terms are CFL and the union of CFLs are closed  , so the language belong to CFL.

Please correct me if I'm wrong.

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Each of them is DCFL but DCFL is not closed under union.

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Thanks for the reply sir..I got it now...