Can I please get the solutions to this Using only the rules

Can I please get the solutions to this

Using only the rules of inference and the logical equivalences, show that the following argument is valid. You may assume that all the premises given are true. Make sure that you include both the rule and the line number(s) to which that rule is applied. You are also expected to define each predicate. Note that each of the premises and the conclusion must be translated into quantified statements. The universe of discourse is all animals. Given Animals that live in the swamp can swim. Some rats live in the swamp. All rats have large teeth. Show There is a rat that has large teeth and can swim.

Solution

Let say

1) Animal that live in swamp {P}, can Swim {Q} ::: So it is P-> Q relation

2) Some Rats{R} live in the Swamp , So as Rats are also animal so by Reflexivity law Rat is an Animal .

3) So R belongs to P and Can swim : R -> Q .

4) All rats have large teeth : R -> S(R)

So from statements 3 and 4

there is a rat (R) which can swim and has large teeth.

So