# Any popular television series that is groundbreaking is critically acclaimed. But not all popular television series a...

on October 6 at 12:44PM

Why E is incorrect?

The argument of C and E seems very similar to me, both looks right. Please explain:)

Irina on October 7 at 01:30AM

Let's look at the structure of the argument.

Any popular television series (P) that is groundbreaking (Q) is critically acclaimed (R)

P ^ Q -> R

Contrapositive of this statement is :

~R -> ~P v ~ Q

If a show is not critically acclaimed, it is either not popular or not groundbreaking.

But not all popular television series are critically acclaimed.

This statement tells us that P is true but R is false - popular but not acclaimed. We can see from the first premise, that if R is false, then either P or Q must be false:

~ R -> ~P v ~ Q

Since we know that P is true, we can conclude that Q is false (not all shows are groundbreaking)

Therefore, ~Q.

Let's look at the pattern of reasoning in (C) & (E):

(C) If biography is unbiased (P), it contains embarrassing facts (Q) about the subject.

P -> Q

The contrapositive of this premise is:

~Q -> ~P

Since not all biographies contain embarrassing facts (~Q), then not all biographies are unbiased.

~Q
Therefore, ~ P

This is a valid argument, per premise (1), we can conclude that if ~Q is true, then ~P is true.

Let's compare it to (E):

If a book is worth reading (P), it is worth buying (Q)

P -> Q

Since not all books are worth reading, not all books are worth buying

~P
Therefore, ~Q

This is in an invalid argument as it commits a logical fallacy of mistaken reversal. We can only conclude that ~Q -> ~P (a proper contrapositive of the first premise), we cannot conclude ~Q when ~P is true.

Let me know if this makes sense and if you have any further questions.

~