Select the option, which is the logical equivalent of the statement gi

Select the option, which is the logical equivalent of the statement given below:If the train is late then I will come by taxi.1. If the train is not late then I will not come by taxi.2. If the train is not late then I will come by taxi.3. If I come by taxi then the train must be late.4. If I do not come by taxi then the train must not be late.

Answer» Correct Answer - Option 4 : If I do not come by taxi then the train must not be late.

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 : train is late

q : I will come by taxi

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 train is late then I will come by taxi." logical equivalent statement is "If I do not come by taxi then the train must not be late.".

Hence, option 4 is the correct answer.

NOTE:

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