i. Let p : It rains, q : the match will be cancelled.
\(\therefore\)The symbolic form of the given statement is p\(\rightarrow\)q.
Converse: q\(\rightarrow\)p
i.e., If the match is cancelled then it rains.
Inverse: ~p\(\rightarrow\)~q
i.e., If it does not rain then the match will not be cancelled.
Contrapositive: ~q\(\rightarrow\)~p i.e. If the match is not cancelled then it does not rain.
ii. Let p: A function is differentiable,
q: It is continuous.
\(\therefore\)The symbolic form of the given statement is p\(\rightarrow\)q.
Converse: q\(\rightarrow\)p
i.e. If a function is continuous then it is differentiable.
Inverse: ~p\(\rightarrow\)~q
i.e. If a function is not differentiable then it is not continuous.
Contrapositive: ~q\(\rightarrow\)~p
i.e. If a function is not continuous then it is not differentiable.
iii. Let p: Surface area decreases,
q: The pressure increases.
\(\therefore\)The symbolic form of the given statement is p\(\rightarrow\)q
Converse: q\(\rightarrow\)p
i.e. If the pressure increases then the surface area decreases.
Inverse: ~p\(\rightarrow\)~q
i.e. If the surface area does not decrease then the pressure does not increase.
Contrapositive: ~q\(\rightarrow\) ~p
i.e. If the pressure does not increase then the surface area does not decrease.
iv. Let p: A sequence is bounded,
q: It is convergent.
\(\therefore\)The symbolic form of the given statement is p\(\rightarrow\)q
Converse: q\(\rightarrow\)p
i.e. If a sequence is convergent then it is bounded.
Inverse: ~p\(\rightarrow\)~q
i.e. If a sequence is not bounded then it is not convergent.
Contrapositive: ~q\(\rightarrow\)~p
i.e. If a sequence is not convergent then it is not bounded.
