score: 6/10 answered: 7/10 question 8 draw a set diagram to determine whether the conclusion follows…

score: 6/10 answered: 7/10 question 8 draw a set diagram to determine whether the conclusion follows logically from the premises. some cats go to heaven. shadow is not a cat. therefore, shadow will not go to heaven. valid argument invalid argument all cows eat grass. all animals that eat grass live outdoors. therefore, all cows live outdoors. valid argument invalid argument question help: message instructor check answer

score: 6/10 answered: 7/10 question 8 draw a set diagram to determine whether the conclusion follows logically from the premises. some cats go to heaven. shadow is not a cat. therefore, shadow will not go to heaven. valid argument invalid argument all cows eat grass. all animals that eat grass live outdoors. therefore, all cows live outdoors. valid argument invalid argument question help: message instructor check answer

Answer

Explanation:

Step1: Analyze first - set of statements

Let set $C$ be cats, set $H$ be things that go to heaven. The first statement is $C\cap H\neq\varnothing$. The second statement is that Shadow $\notin C$. Just because Shadow is not a cat, we cannot conclude Shadow $\notin H$ since there are non - cat things that could go to heaven. So the first argument is invalid.

Step2: Analyze second - set of statements

Let set $C$ be cows, set $G$ be grass - eating animals, and set $O$ be animals that live outdoors. The first statement is $C\subseteq G$, the second statement is $G\subseteq O$. By the transitive property of set inclusion, if $A\subseteq B$ and $B\subseteq C$, then $A\subseteq C$. So $C\subseteq O$, which means all cows live outdoors. The second argument is valid.

Answer:

  1. B. Invalid argument
  2. A. Valid argument