Please dont answer if your not 100 sure ty prove each statem

Please don\'t answer if your not 100% sure! ty

prove each statement. Each line should be a different identity. A U (B U B) = U A U B n B = A n B Let D = {0, 1}, express the elements of D^3 as a string and not as n-tuple. Let D = {0, 1}, what is |D^4|? Remember to include work in answer as a statement.

Solution

I a)

L.H.S. = A U (B U B\')

from complement\'s law, B U B\' = U, we have

= A U U = U (Domination law)

= R.H.S.

b) L.H.S. = (A U B\')\' B = (A\' B\'\') B (from Demorgan\'s law)

= (A\' B) B = A\' (B B) = A\' B (from Idemoptent\'s law)

= R.H.S.