Indicate whether the arguments are valid or invalid. Support your answers by drawing diagrams.

a. All thoughtful people can tell a valid argument from an invalid one.
b. All discrete mathematics students are thoughtful.
c. All discrete mathematics students can tell a valid argument from an invalid one.

Invalid in tha way from a and b we can conclude c.

In the other way, from a and c we can NOT conclude b.

Step-by-step explanation:

We have 3 sets: 1.people who can tell a valid argument from an invalid one

2.thoughtful people and 3.discrete mathematics.

From a. we concluded that 2. set is subset of 1. set.

From b. we concluded that set 3. is subset of set 2.

Now we know that set 3. must be subset of the set 1. That implicate that c is valid. (diagram 1)

If we want to conclude from a and c the b, it is not possible, because we dont have all informations.

From a. we know thah set 2. is subset od set 1.

From c. we know that set 3. is also subset of set 1.

But it does not follow that 3. is subset of set 2. (diagram 2)

the probability is 0