Thank you gaurav but if it is given that no cats are rat then it also means that no rats are cats. let us take an example, A not equal to B then it also means that B not equal to A.
we can give the problem an another look like this suppose CAT as A, RAT as B and DOG as C.
Now it is given that No A is B means that A not equal to B,
again given is No B is C means that B not equal to C.
So, interpretation is A not equal to B and B not equal to C.
Hence, We can't define the relationship between the A and C.
e.g. LET the value of A=5, B=15 and C=7.
given is A=!B and B=!C (*Here =! means not equal to)
By seeing above values, values satisfy the given condition So we can say A=!C thish is first result say.
Let another value of A=60, B=10 and C=60.
again given is A=!B and B=!C.
By seeing the values, again values satisfy the above equation So we can say tha A=C.
Now we have obtained two different contradicting results A=!C and A=C for the same given condition.
So, we conclude that might be No A is C or might be A is C.
Result can't be determined.