Question

I will return to college. j i will get a job. translate the following english sentences into logical expressions using the definitions above

(a) not getting a job is a sufficient condition for me to return to college
(b) if i return to college, then i won't get a job
(c) i This problem has been solved

Answer 1

To translate the given English sentences into logical expressions, you can use the following expressions: ¬J ⇒ R, R ⇒ ¬J, and R ⇔ ¬J.

Step-by-step explanation:

a) The logical expression for 'not getting a job is a sufficient condition for me to return to college' can be written as: ¬J ⇒ R. Here, ¬J represents 'not getting a job' and R represents 'returning to college'.

b) The logical expression for 'if I return to college, then I won't get a job' can be written as: R ⇒ ¬J. Here, R represents 'returning to college' and ¬J represents 'not getting a job'.

c) The logical expression for 'I will return to college if and only if I won't get a job' can be written as: R ⇔ ¬J. Here, R represents 'returning to college' and ¬J represents 'not getting a job'.

The student is asking for help in translating given English sentences into logical expressions. The first sentence states that not getting a job is a sufficient condition for returning to college, and can be represented by the logical expression ~j -> i, where '->' denotes 'implies'. The second sentence, if I return to college, then I won't get a job, can be represented by i -> ~j.

The definitions provided are as follows: i means 'I will return to college', and j means 'I will get a job'. In logical expressions, the '~' symbol represents 'not'. Using these, we can create logical expressions that represent the given English statements.