Question

State the converses of the following propositions, and indicate which of them are equivalent to the given propositions:

Answer 1

Explanation:

Note that, stating the converse of a statement in logic simply involves you reverse the initial two statements (hypothesis &conclusion [S&P]).

a. No people who are considerate of others are reckless drivers who pay no attention to traffic regulations.

We could deduce from this statement that the equivalent (reverse) to be:

No S is P ≥ No P is S (where S represents the hypothesis, and P represents the conclusion)

The converse read; No reckless drivers are considerate of others.

b. All graduates of West Point are commissioned officers in the U.S. Army.

We could deduce from this statement that the equivalent (reverse) to be:

All S is P -> Some P is S

The converse read; Some commissioned officers of West Point are graduates

c. Some European cars are overpriced and underpowered automobiles.

We could deduce from this statement that the equivalent (reverse) to be: Some S are P -> Some P is S

The converse read;  Some overpriced cars and underpowered automobiles are European cars

d. No reptiles are warm-blooded animals.

We could deduce from this statement that the equivalent (reverse) to be:

No S is P -> No P is S

The converse read; No warm-blooded animals are reptiles.

e.  Some professional wrestlers are elderly persons who are incapable of doing an honest day’s work

We could deduce from this statement that the equivalent (reverse) to be: Some S is P -> Some P is S

The converse read; Some elderly persons are professional wrestlers