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.”

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