Gate Exam

Which of the following is TRUE?

Option
(A) Every relation in 3NF is also in BCNF
(B) A relation R is in 3NF if every non-prime attribute of R is fully functionally dependent on every key of R
(C) Every relation in BCNF is also in 3NF
(D) No relation can be in both BCNF and 3NF

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Gate Other Question
After several defeats in wars, Robert Bruce went in exile and wanted to commit
suicide. Just before committing suicide, he came across a spider attempting
tirelessly to have its net. Time and again, the spider failed but that did not deter
it to refrain from making attempts. Such attempts by the spider made Bruce
curious. Thus, Bruce started observing the near-impossible goal of the spider to
have the net. Ultimately, the spider succeeded in having its net despite several
failures. Such act of the spider encouraged Bruce not to commit suicide. And
then, Bruce went back again and won many a battle, and the rest is history.
Which one of the following assertions is best supported by the above information?
(A) Failure is the pillar of success
(B) Honesty is the best policy
(C) Life begins and ends with adventures
(D) No adversity justifies giving up hope Assuming P ≠ NP, which of the following is TRUE?

Option
(A) NP-complete = NP
(B) NP-complete © P = null
(C) NP-hard = NP
(D) P = NP-complete