Using Truth Table to conclude.

Question

I have made this truth table for the following propositions.

While scouting and investigating the flora of an island, biologists identified Three species of plants of particular interest: Dahlia, Crocus and Snowdrop. The biologists made the following observations:

1. If Dahlias grow in an area, Crocus will also grow in that area.
2. Either Crocus or Snowdrops grow in an area (i.e. but they never grow together in that area).
3. Dahlias or Snowdrops always grow in an area.

I Convert aforementioned observations into propositional formula. I Relying on a truth table, identify which plants can grow in the different areas of the Island (i.e: which plants of interest can you find in an area of the Island?)

The question is asking

Relying on a truth table, identify which plants can grow in the different areas of the Island (i.e: which plants of interest can you find in an area of the Island?)

I don't understand how I can use the table to see which plants can grow in the different areas of the island. Any help would be appreciated.

Answer 1

Without realizing it, you have solved the problem.

The whole point of the truth table approach is that only those rows where the computed values are all True are acceptable. These rows represent the rows where all of the constraints are satisfied.

You have already determined this.

Your rightmost computed column shows that only rows $2$ and $7$ satisfy the constraints.

These represent the following possibilities:

• Dahlia, Crocus, and not Snowdrop

• Snowdrop only.