Which of the following arguments (i.e. logical calculations) reach logically valid conclusions, and which do not? Which argument utilizes the logical rule of modus ponens?

A. My boss is busy at the moment is the contradiction of My boss is available at the moment

B. My boss is busy at the moment is the contradictory of My boss is available at the moment

C. My boss is busy at the moment is the contradictory of My boss is not available at the moment

A. (p q) = (q p)

B. (p q) (q p)

C. (q p) (p q)

D. (p q) & (q p)

A. Meanings

B. Language system

C. Senses

D. Utterances

A. Before – after

B. Borrow – lend

C. Sad – happy

A. Afternoon

B. Carpenter

C. Vision

A. Beneficiary

B. Affected

C. Instrument

A. The propositional connective & corresponds roughly to if . . . then

B. The propositional connective -> corresponds roughly to if . . . then

C. The propositional connective -> corresponds roughly to and