5. Puzzling puffins Your biologist friend is convinced about the following behavioral trait of puffins: If it is summer, then puffins come back to land, and if puffins come back to land, then the puffins will make burrows, which means that if it is summer, then puffins will make burrows. You might not be a biologist, but you can use your logic skills to verify this claim! (a) Translate the proposition to the equivalent statement in propositional logic. For simplicity, let s, [ and b be the following propositions: e s: It is summer e [ : Puffins come back to land e b : Puffins will make burrows (b) Translate the proposition without using and using only V, A and as needed (make sure to have the negation entered inside the parenthesis). () Is your biologist friend correct about this claim? Justify your answer using a truth table. (Hint: Check if the expression is a tautology) (d) Suppose that it is not the case that puffins coming back to land imply that they will make burrows. Is this logically equivalent to saying that if puffins come back to land, then they will not make burrows? Specifically, verify if: (l>b)=l-b Either provide an assignment of truth values to [ and b that shows that they are not logically equivalent, or prove using the laws of logic that they are logically equivalent, indeed