Solution to prove a --> ( b V c ) using contradiction method and combination of inference … - Sikademy
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Archangel Macsika

prove a --> ( b V c ) using contradiction method and combination of inference rules and equivalence laws from these premises : 1. a --> ( d V b ) 2. d --> c

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Let us prove using the method by contradiction.

Suppose that the premises a \to ( d \lor b ) and d \to c are true, but the conclusion a \to( b \lor c ) is false.

The definition of implication implies a is true and b\lor c is false, and hence definition of disjunction implies b is false and c is false. Since d \to c is true and c is false, we conclude that d is false. Consequently, d\lor b is false, and thus a \to ( d \lor b ) is false. This contradiction proves the premises a \to ( d \lor b ) and d \to c imply the conclusion a \to( b \lor c ).

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