119 views

Choose the correct alternatives (More than one may be correct).

Indicate which of the following well-formed formulae are valid:

1. $\left(P\Rightarrow Q\right) {\wedge} \left(Q \Rightarrow R\right) \Rightarrow \left(P \Rightarrow R\right)$
2. $\left(P\Rightarrow Q\right) \Rightarrow \left( \neg P \Rightarrow \neg Q\right)$
3. $\left(P{\wedge} \left(\neg P \vee \neg Q\right)\right) \Rightarrow Q$
4. $\left(P \Rightarrow R\right) \vee \left(Q \Rightarrow R\right) \Rightarrow \left(\left(P \vee Q \right) \Rightarrow R\right)$

A is true it is Hypothetical syllogism.

In classical logic, hypothetical syllogism is a valid argument form which is a syllogism having a conditional statement for one or both of its premises. If I do not wake up, then I cannot go to work. If I cannot go to work, then I will not get paid. Therefore, if I do not wake up, then I will not get paid.

+1 vote
Create a logic table for each of the given formula and check if we are getting true everywhere.