Verify each of the following equivalences by writing an equi

Verify each of the following equivalences by writing an equivalence proof. Thai is, start on one side and use known equivalences to gel to the other side. A rightarrow B C (A rightarrow B) (A rightarrow C).

Solution

From the following truth table, it is clearly evident that a implies (b or c) is equivalent of (a implies b) or (a implies c)

a T T T T F F F F

b T T F F T T F F

c T F T F T F T F

b or c T T T F T T T F

a implies ( b or c) T T T F T T T T

a implies b T T F F T T T T

b implies c T F T F T T T T

(a implies b) or (b implies c) T T T F T T T T