Concept
How can every professor being human be expressed correctly?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"35. True or false: ∀ x Professor ( x ) ⇒ Human ( x ) . True at last! This is what we were try- ing to say all along. Every professor is a person. 36. True or false: ¬∃ x Professor ( x ) ⇒ ¬ Human ( x ) . True! This is an equivalent statement to item 35. There’s nothing in the universe that is a professor yet not a human. (At least, at the time of this writing.)"
Related Ideas
- How can quantifiers be negated, interchanged, and ordered?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- 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
- How do universal and existential quantifiers express claims about many objects?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- How do implication and equivalence work in propositional logic?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- What does ¬∃ x Human(x) mean?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- What does ¬∀ x Human ( x ) . True mean?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- Why is the statement “nothing is human” false?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- Why is the assertion X ∧ ¬ Y ∧ ¬ ( Z ⇒ X ) impossible?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1