# Prove that every problem in P is reducible

1,628

You've sort of answered your own question.

"$A$ is reducible to $B$" means "Given a black box that solves problem $B$ in constant time, we can solve problem $A$ in polynomial time." Since $A$ is in $P$, this statement is always true: we can simply throw away our black box to $B$ and solve $A$ without it.

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### Takkun

Updated on June 15, 2022

• Takkun less than a minute

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For two problems A and B, if A is in P, then A is reducible to B?

Given two problems $A$ and $B$, if $A$ is in $\def\P{{\mathcal P}}\P$ then $A$ is reducible to $B$. ($A < B$)

Why does it not matter if $B$ is in $\P$ or $\mathcal{NP}$?
Why can just knowing that $A$ is in $\P$ mean that it is reducible regardless of $B$?

• Erick Wong over 9 years
Please state your definition of reducible. In these questions it is vital that you know what the terms mean with great precision.
• Takkun over 9 years
Thanks, rewriting it like that clears up some of my confusion.
• eva over 7 years
I have a question regarding this answer: Why does B have to be solved in constant time?