Question

Logical equivalence of two English statements.

Define the following propositions:
j: Sally got the job.
l: Sally was late for her interview
r: Sally updated her resume.
Express each pair of sentences using a logical expression. Then prove whether the two expressions are logically equivalent.
If Sally did not get the job, then she was late for interview or did not update her resume.
If Sally updated her resume and was not late for her interview, then she got the job.

Answer 1

The logical expressions for the given sentences are: If Sally did not get the job, then (she was late for interview OR did not update her resume). If (Sally updated her resume AND was not late for her interview), then she got the job. These expressions are logically equivalent.

Step-by-step explanation:

The logical expressions for the given sentences are:

1. If Sally did not get the job, then (she was late for interview OR did not update her resume).

2. If (Sally updated her resume AND was not late for her interview), then she got the job.

To prove whether these two expressions are logically equivalent, we can use a truth table. By evaluating the truth values of both expressions for all possible combinations of truth and falsity of their constituent propositions (j, l, and r), we can determine if the two expressions always have the same truth value.

Using a truth table, we find that both expressions have the same truth values for all possible combinations, which means they are logically equivalent.