The claim conflates asymptotic complexity classes with concrete algorithmic equivalence: P=NP would mean SAT is solvable in polynomial time, making it strictly easier than truth table construction, not equally hard.

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Asymptotic complexity classes(computer science and mathematics): A way of categorizing how the time or resources needed to solve a problem grows as the problem gets bigger—focusing on the long-term trend rather than exact numbers.
P=NP(mathematics and computer science): A famous unsolved question in computer science asking whether two classes of problems (P and NP) are actually the same—if true, it would mean certain very hard problems can actually be solved quickly.
SAT (Boolean satisfiability problem)(in computational logic): A famous computer science problem that asks: can you assign true or false values to variables in a logical formula to make the whole thing true?
Truth table construction(computer science and logic): A brute-force method where you check every possible combination of true/false values to see which ones work—simple but can take an extremely long time for large problems.

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