Concept
Why are ∀ x Human(x) ∧ Professor(x) and ∀ x Human(x) ⇒ Professor(x) different?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"32. True or false: ∀ x Human ( x ) ∧ Professor ( x ) . Not even close. This says “everything in the universe is a human professor.” (Even though I would exist in such a world, what a sad, limited place it would be.) 33. True or false: ∀ x Human ( x ) ⇒ Professor ( x ) . False. This says “every person is a professor.” (Consider LeBron James.) Keep in mind: “ ∀ ” and “ ∧ ” don’t really play well together."
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