Proving Set Equality: {A ∪ (B ∩ C')} ∪ A ∪ C = A

khoo · May 25, 2017

Prove that {A UNION(B INTERSECT C')} UNION (A UNION C)=A

HallsofIvy · May 26, 2017

You can't prove it, it's not true! Let the "universe" be {1, 2, 3, 4, 5}, A= {1, 2, 3}, B= {1, 3, 4}, and C= {5}. Then C' is {1, 2, 3, 4} which contains B so B union C' is {1, 2, 3, 4}. A union (B union C')= {1, 2, 3, 4}. A union C is {1, 2, 3, 5} so (A union (B union C')) union (A union C) is {1, 2, 3, 4, 5}, NOT A.

Proving Set Equality: {A ∪ (B ∩ C')} ∪ A ∪ C = A

Graduate Expected numbers of cards of a last color remaining

Graduate Probability puzzle

Undergrad The problem of points

Undergrad The countability paradox of computable numbers

Undergrad How does axiom of foundation prevent infinite sequence of elements?

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Proving Set Equality: {A ∪ (B ∩ C')} ∪ A ∪ C = A

Similar threads