Question

Consider the statement “If you break it, then you fix it”.

Select which one of the following statements is not logically equivalent to that conditional, or select All of these statements are equivalent to “If you break it, then you fix it”.

Group of answer choices

All of these statements are equivalent to “If you break it, then you fix it”.

You fix it only if you break it.

Fixing it is a necessary condition for having broken it.

Breaking it is a sufficient condition for having to fix it.

If you are not fixing it, then you didn’t break it.

You didn’t break it unless you are fixing it.

Answer 1

Statement :- IF YOU BREAK IT, THEN YOU FIX IT.

Consider 'You break it' as P and 'You fix it' as Q. Then

Truth Table

P	Q
T	T	T	T
T	F	F	T
F	T	T	F
F	F	T	T

i) 'You fix it only if you break it.' (Q only if P) is NOT equivalent.

ii) 'Fixing it is a necessary condition for having broken it.'  IS EQUIVALENT TO THE GIVEN STATEMENT.

iii) 'Breaking it is a sufficient condition for having to fix it.' IS EQUIVALENT TO THE GIVEN STATEMENT.

iv) 'If you are not fixing it, then you didn’t break it.' () IS EQUIVALENT TO THE GIVEN STATEMENT.

v) 'You didn’t break it unless you are fixing it.' () (if you not are fixing it, you did not break it.) IS EQUIVALENT TO THE GIVEN STATEMENT. (same as (iv).)