Mathematical Re...

The contrapositive of $$(\sim p\wedge q)\rightarrow \sim r$$ is equivalent to

Consider the. following compound statement
(i) Mumbai is the capital of Rajasthan or Maharashtra,
(ii) $$\displaystyle \sqrt{3}$$ is a rational number or an irrational number,
(iii) $$125$$ is a multiple of $$7$$ or $$8$$
(iv) A rectangle is a quadrilateral or a regular hexagon.
Which of the above statements is not true?

The contrapositive of the statement "If you believe in yourself and are honest then you will get sucess" is

The converse of $$p \rightarrow (q \rightarrow r)$$ is 

The contrapositive of $$\sim p \rightarrow ( q \rightarrow \sim r)$$ is

The negative of the statement "If a number is divisible by $$15$$ then it is divisible by $$5$$ or $$3$$"

In the following letter sequence, some of the letters are missing. These are given in order as one of the alternatives below. Choose the correct alternative.
$$\alpha \beta$$ _$$\alpha \alpha$$ _$$\beta \beta \beta$$ _$$\alpha \alpha \alpha \alpha$$ _$$\beta \beta \beta ...$$

The converse of $$p \rightarrow (q \rightarrow r)$$ is

The negation of the statement $$q \vee  (p \wedge \sim r)$$ is equivalent to 

If statements $$p, q, r$$ have truth values T, F, T respectively then which of the following statement is true