# Did I translate this correctly?

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

• I'm confused. Why have you written 3 logical sentences? Do you want us to pick which one is equivalent to the English you started with? – Nathaniel Mayer Jan 30 at 17:41
• I translated it into a math problem then negate it, then I translated it back into an English statement although translating back into english is not important, just seeing if i understand this.@NathanielMayer – Derek Long Jan 30 at 17:43
• So what's the second sentence? Is it supposed to be equivalent to the first? (It's not) – Nathaniel Mayer Jan 30 at 17:46
• yes I was trying to make it equivalent. is ( ∃x)D(x) /\ (∃x)~C(x not correct?@NathanielMayer – Derek Long Jan 30 at 17:49
• The third one is correct as a negation of the first. It's not a negation of the second – Nathaniel Mayer Jan 30 at 17:50

The second is different from both, not sure what you were doing there. I suspect maybe you were looking for $$\vee$$ instead of $$\wedge$$.