Question

“All dogs are mammals.”

Which of these is a logically equivalent statement?

All animals that are not dogs are not mammals.

If it is not a dog, it is not a mammal.

All dogs are furry.

If it is not a mammal, it is not a dog.

Answer 1

ok does the first one make sense?

"all animals that are not dogs are not mammals". Hint: cats are not dogs, but they are mammals.

Answer 2

The last one is the best choice ^.^
Because dogs are mammals.

Answer 3

thnks

Answer 4

An implication and its contrapositive are logically equivalent.
As an implication, All dogs are mammals" can be written as
If an animal is a dog, then the animal is a mammal.
The contrapositve of that statement is:
If the animal is not a mammal, then the animal is not a dog.
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Answer: If it is not a mammal, it is not a dog.
is logically equivalent to the given statement.

Suggestion: Go to the following link and study a bit about implications:


http://www.regentsprep.org/Regents/math/geometry/GP2/PracRC.htm

Answer 5

right, you should check those out. then all you have to remember is

if P implies Q then, not Q implies not P. it will make life easy:)

note: here we have P = its a dog and Q = its a mammal