# Questions & Answers of Propositional Logic

## Weightage of Propositional Logic

Total 3 Questions have been asked from Propositional Logic topic of Mathematical Logic subject in previous GATE papers. Average marks 1.33.

The statement $\style{font-family:'Times New Roman'}{\left(\neg p\right)\Rightarrow\left(\neg q\right)}$ is logically equivalent to which of the statments below?

I. $\style{font-family:'Times New Roman'}{p\Rightarrow q}$

II. $\style{font-family:'Times New Roman'}{q\Rightarrow p}$

III. $\style{font-family:'Times New Roman'}{\left(\neg q\right)\vee p}$

IV. $\style{font-family:'Times New Roman'}{\left(\neg p\right)\vee q}$

##### Show Answer

Let p,q, and r be proposition and the expression $\style{font-family:'Times New Roman'}{\left(p\rightarrow q\right)\rightarrow r}$ be a contradiction. Then, the expression $\style{font-family:'Times New Roman'}{\left(r\rightarrow p\right)\rightarrow q}$ is

##### Show Answer

Let p, q, r, denote the statements "It is raining". "It is cold", and "It is pleasant", respectivelyThen the statement "It is not raining and it is pleasant, and if it is raining only if it is raining and it is cold" is represented by