Question

Read the statement shown below.

"If Johan completes his project, then he will visit the museum."

- Which of these is logically equivalent to the given statement?

a- If Johan visits the museum, then he did not complete his project.

b- If Johan completes his project, then he will not visit the museum.

c- If Johan did not visit the museum, then he did not complete his project.

d- If Johan did not complete his project, then he will visit the museum.

Answer 1

The correct answer is C. Translating it to logical simbolism, it would be like:

If A, then B. (A= Johan completes his project; B= he will visit the museum)

Then:

a- →B¬A (If B is correct, A is incorrect: If Johan visits the museum, then he didn't complete his project)
b- →A¬B (If A is correct, B is incorrect: If Johan completes his project, he won't visit the museum)
c- ¬A¬B (If A is incorrect, B is incorrect → If A is correct, B is correct: initial statement)
d- ¬A→B (If A is incorrect, B is correct: If Johan did not complete his project, he will go to the museum)

a→b (If a then b)
a¬b (If a then no b)


Mathematical logic is an amazing mathematics subfield :)