**((P=>Q) ^ (Q => R)) => (P => R) ** named **Hypothetical Syllogism**

P => Q (if P imples Q and…)

Q => R (if Q implies R…)

Then, P must imply R.

P = I do not wake up

Q = I cannot go to work.

R = I will not get paid.

If I do not wake up, then I cannot go to work. (P => Q)

If I cannot go to work, then I will not get paid. (Q => R)

Therefore, if I do not wake up, then I will not get paid. (P => R)

3 no namers – logical implications

Hypothetical Syllogism – a logical implication

Disjunctive Syllogism – a logical implication

Simplification – a logical implication

Addition – a logical implication

Modus tollens – a logical implication

Modus ponens – a logical implication

Logical Implications