Consider the proposition: “If someone in your class has a dog, then everyone in your class has a cat.”
-Translate this sentence into mathematics, letting D(x)
be the predicate “x has a dog”, C(x) be the predicate “x has a cat.”
Let the universe of discourse be the set of students in your class.
~=not, /\=and,/=or, ->=arrow
- negate:( ∃x)D(x) -> (∀x)C(x)
- ~( ∃x)D(x) \/(∀x)C(x)
- ( ∃x)D(x) /\ (∃x)~C(x)
- translated back into english:
some student have a dog and some students do not have a cat
Best Answer
The first sentence you wrote is an accurate translation, and the third sentence is the correct negation of the first.
The second is different from both, not sure what you were doing there. I suspect maybe you were looking for $\vee$ instead of $\wedge$.