Determine whether the following set equivalence is true (A \cup B) \ (A \cap C) = B

Jason Farmer

Jason Farmer

Answered question


Determine whether the following set equivalence is true
(AB) (AC)=B(A C)

Answer & Explanation



Skilled2021-08-21Added 83 answers

Step 1
Consider the RHS of the given equation.
B(AC)=B(ACc) [Apply the rule AB=ABc]
=(BA)(BCc) [Distributive Law]
Consider the LHS of the given equation as follows.
(AB)(AC)=(AB)(AC)c [Apply the rule AB=ABc]
=(AB)(AcCc) [Apply De Morgan's Law]
Step 2
Construct truth table for LHS and RHS as follows.
Observe the last columns of the both truth tables. The first truth value of the first row last column of both truth tables are not the same.
Thus the given set equivalence is not true.

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