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

Irina on October 7, 2019

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.



~

on January 21, 2021

I am still not understanding why is E is incorrect?