Question

1. Using predicate logic, prove that each argument in Exercises 29-37 is valid. Use the predicate symbols shown.
36. Some elephants are afraid of all mice. Some mice are small. Therefore there is an elephant that is afraid of something small. E(x), M(x), A(x, y), S(x)

Answer 1

The two given premises can be translated into predicate logic as follows:

1. 
2. 

The inference we need to obtain is:

• 

We instantiate e in premise 1 to obtain

and we instantiate m in premise 2 to obtain

.

From [b] we get

and

.

So from [a] and [c] we obtain

and combining [d] and [e] we get

.

Generalizing [f] we obtain the inference: