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1 simplify the following expressions

1. z=abc+abc'+ab'c

2. x=(a'+b)(a+b+d)d'

2. apply de morgan's therems and simplify

1. z=(a(a+c')')'d

2. z=abc+ab'(a'c')'

3. z=(a+b=b'cd')'+b'cd'

4. z+a'c(a'bd)'+(a'bc'd'+ab'c)'

3. implement the following boolean expressions using and,or,not

1. x=b'c+ac+ab'

2. x=(a'+b'+c)+ab