Puzzle/Logic Question

Question

Harry, Emily, Grace, and Rohit each have a pet, and have picked a unique number from 1 to 4. Using the following clues, match each person with their pet and number.

(a) Emily owns the cat or the dog.

(b) Grace owns the Lizard.

(c) The bird owner picked the number 2 more than Rohit's number.

(d) The dog owner picked the 3.

Does my conclusion make sense?

My Solution:

Since Grace is stated to own the lizard, she is the one with the lizard.

Emily owns the cat or the dog, so I said she would have the dog.

Harry owns the bird because Rohit doesn't own an animal yet. Therefore, Rohit has the cat.

Since Emily is the dog owner she has #3.

Rohit must have two because two more would either be four or three, and it cannot be one because three is already assigned, and Harry has #2 leaving Grace with #1.

$\therefore$ Grace owns a lizard, #1. Rohit owns the cat, #2. Emily does own the dog, #3. Harry owns the bird, #4.

Answer 1

From "Grace owns a lizard" we know that Rohit does not own a lizard.

From "The bird owner picked a number two more than Rohit's number" we know that Rohit does not own a bird. (There is no number two larger than itself) Further, we know that Rohit picked a $2$ or a $1$ since otherwise there is no valid number for the bird owner to have picked.

From our conclusion that Rohit's number is a $2$ or a $1$ as well as "The dog owner picked a $3$" we know that Rohit did not pick a dog.

Based on these three previous observations, since Rohit cannot have picked any of a lizard, a bird, or a dog, but Rohit must have picked something, the only thing remaining that Rohit could have picked was a cat.

Since the dog owner was the one who picked a $3$, it cannot be the case that the bird owner also picked a $3$. Therefore Rohit must have picked a $2$ and not a $1$ to avoid the bird owner from having picked a $3$. We learn also then that the bird owner picked a $4$.

Rohit - Cat - $2$

Since Rohit picked the cat and Emily can not have also picked the cat, from "Emily picked a cat or a dog" we know then that Emily must have picked the dog and from "The dog owner picked $3$" we know that Emily picked the dog and #3.

Emily - Dog - $3$

Since someone must have picked the bird and it wasn't any of Grace, Rohit, or Emily, it must have been Harry who picked the bird. Combined with earlier observations, we have then that Harry picked the bird and $4$.

Harry - Bird - $4$

Finally, Grace with the lizard receives the final remaining number, $1$.

Grace - Lizard - $1$

Answer 2

I think assuming harry has bird because he did not have an animal till that point does not seem correct although you did reach the correct answer using this conclusion. What I do in these questions is build a table and fill all the info mentioned and cross out impossible options. Then like here for emily we had 2 choices, so either we could assume pne option to be correct and proceed or in this case I inferred from the 3rd and 4th clue that rohit cannot own a dog.