YES!!!!

Here is a direct proof as well as a truth table. Enjoy!

(A and not ( B or C)) or (B or C) = <--- given

(A and not B and not C) or (B or C) = <--- DeMorgan's

Distributive

A or (B or C) and [not B or (B or C)] and [not C or (B or C)] =

Associative

A or (B or C) and [not B or B or C] and [not C or B or C] =

Cancellation/Asportion Property : X or not X must be true; third var gets eaten

A or (B or C) and True and True

Absoprtion Property: outcome depends entirely on A or (B or C)

A or (B or C)

Truth Table:

A B C B or C !(B or C) A and !(B or C) RHS A or B or C

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T T T T F F T T

T T F T F F T T

T F T T F F T T

T F F F T T T T

F T T T F F T T

F T F T F F T T

F F T T F F T T

F F F F T F F F