title: When to use conjunction and when to use implication? (First Order Logic)
body: <p>I'm learning First Order Logic at the moment. I'm looking at this example:</p>
  
  <p>Some dogs bark
  ∃x (dog(X) Λ bark(x))</p>
  
  <p>All dogs have four legs
  ∀x (dog(x) -> have_four_legs(x))</p>
  
  <p>My question is: is it possible for the second example to be:
  ∀x (dog(x) Λ have_four_legs(x))</p>
  
  <p>And why can't the first example be:
  ∃x (dog(X) -> bark(x))</p>