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boolean algebra
- 18. Solution Reason x + x = ( x + x ) 1 Basic identity (b) = ( x + x ) ( x + x’) Basic identity (a) = x + xx’ Distributive (b) = x + 0 Basic identity (b) = x Basic identity (a)
- 19. Solution Reason x . x = xx + 0 Basic identity (a) = xx + xx’ Basic identity (b) = x (x + x’ ) Distributive (a) = x . 1 Basic identity (a) = x Basic identity (b)
- 20. Solution Reason x + 1 = (x+1) . 1 Basic identity (b) = (x+1) . (x + x’) Basic identity (a) = x + 1x’ Distributive (b) = x +x’ Basic identity (b) = 1 Basic identity (a)
- 21. Solution Reason x . 0 = x.0 + 0 Basic identity (a) = x.0 + xx’ Basic identity (b) = x ( 0 + x’ ) Distributive (a) = x ( x’ ) Basic identity (a) = 0 Basic identity (b)
- 23. Solution Reason x + xy = x.1 + xy Basic identity (a) = x( 1 + y ) Distributive (a) = x (y+ 1) Commutative (a) = x .1 Basic identity (a) = x Basic identity (b)
- 24. Solution Reason x ( x + y ) = xx + xy Distributive (a) = x + xy Basic identity (b) = x1 + xy Basic identity (b) = x ( 1 + y ) Distributive (a) = x.1 Basic identity (a) = x Basic identity (b)