Concepts:

If 'p' then 'q' , denoted by p → q where p and q are the hypothesis and conclusion respectively.

p → q denotes implies also,

~ p denotes not p means negation

~ q denotes not q means negation

q → p denotes converse, which means if q then p.

the converse is not true even if the implication is true.

~ p → ~ q denotes inverse, which means if not p then not q.

the inverse is not true even if the implication is true. 

~ q → ~ p  contrapositive,

the contrapositive is true if the implication is true and vice versa.

Given:

p : TV is on

q : switch off the radio

Truth table 

Where T is true denotes positive statement and F is False denotes the negative statement,

The logical equivalence from the truth table :

Implication and contrapositive result is the same i.e, if p happens then q will happen which implies if q won't happen then p also won't happen.

Thus "If the TV is on then Amit will switch off the radio." logical equivalent statement is "If Amit does not switch off the radio then TV must not be on.".

Hence, option 3 is the correct answer.

NOTE:

This is not an english language problem, It is about discrete mathematics proposition logic equivalence.