title: Difference between ∀x∃y and ∃y∀x
body: <p>I'm currently reading this document by the University of Texas in Austin about Predicate Logic, and got stuck on the following: <br></p>
  
  <p>Note about nested quantifiers: For predicate P (x, y): ∀x∀yP (x, y) has the same meaning as ∀y∀xP (x, y). ∃x∃yP (x, y) has the same meaning as ∃y∃xP (x, y).</p>
  
  <p>We can not interchange the position of ∀ and ∃ like this! <br><br>
  Example: U = set of married people. True or false? <br>1. ∀x∃y[x is married to y]<br>
  2. ∃y∀x[x is married to y]</p>
  
  <p>I'm doubtful about the answer to this example. Also, some explanation about ordering of ∃ and ∀ operators would be appreciated. </p>