Answer to Question #286410 in Discrete Mathematics for Sulav Dahal

Question

Use rules of inference to show that the hypothesis "All lions are fierce","Some Lions do not drink coffee" imply the conclusion "Some fierce creatures do not drink coffee".

Answer 1

Solution:

Let’s let L(x) be “x is a lion,” F(x) be “x is fierce,” and C(x) be “x drinks coffee.”

$\begin{aligned} \text { All lions are fierce. } & \forall x(L(x) \rightarrow F(x)) \\ \text { Some lions do not drink coffee. } & \exists x(L(x) \wedge \neg C(x)) \\ \text { Some fierce creatures do not drink coffee. } & \exists x(F(x) \wedge \neg C(x)) \end{aligned}$