Questions & Answers of Propositional Logic

Question No. 1

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

Question No. 29

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

Question No. 111

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