Question

Select the statement that is NOT equivalent to-- "It is not true that England and Africa are both countries."

Answer 1

The original statement is true only if:

• England is a country and Africa isn't
• Africa is a country and England isn't
• Neither of them are countries

Options a and d are equivalent:

$P\implies Q \iff \lnot Q \implies \not P$

and they both are true in the same cases as above.

Option c is also fine, because it is false only if both England and Africa are both countries, just like the original statement.

Option b, instead, is true only if neither of the two options are countries, so it doesn't cover the cases where only one of the two is a country.