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Answer for the clue "Logical system error mostly with unfruitful broken lab gear ", 15 letters:
boolean algebra

Word definitions for boolean algebra in dictionaries

Wikipedia Word definitions in Wikipedia
In mathematics and mathematical logic , Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false , usually denoted 1 and 0 respectively. Instead of elementary algebra where the values of the variables ...

Usage examples of boolean algebra.

This was an animated introduction to sets, leading into Boolean Algebra, with color as an additional tool.

Amrita was retreating into a world of number theory and Boolean Algebra.

The actual content was zero, as honest metaphysics must be, but I loaded it with Boolean algebra, which (if solved) proved that Dzhugashvili was a murdering scoundrel.

It went through physics, astronomy, molecular biology, inorganic chemistry, differential calculus, and Boolean algebra like hydrochloric acid through gossamer.