“if and only if” is an unusual and sometimes confusing way to say it, but the words do directly imply the technical definition.
“it’s an apple if and only if it’s a fruit” literally means “it’s an apple if it’s a fruit” and “it’s an apple only if it’s a fruit”. You already seem to understand the 2nd part, so no need to explain that.
The first part is a bit confusing because the words are in the reverse order compared to how people normally talk. “it’s an apple if it’s a fruit” means the same thing as “if it’s a fruit, then it’s an apple”. Clearly “if it’s a fruit, then it’s an apple” is not a true statement, because there are plenty of other fruits apart from apples.
“if and only if” is an unusual and sometimes confusing way to say it, but the words do directly imply the technical definition.
“it’s an apple if and only if it’s a fruit” literally means “it’s an apple if it’s a fruit” and “it’s an apple only if it’s a fruit”. You already seem to understand the 2nd part, so no need to explain that.
The first part is a bit confusing because the words are in the reverse order compared to how people normally talk. “it’s an apple if it’s a fruit” means the same thing as “if it’s a fruit, then it’s an apple”. Clearly “if it’s a fruit, then it’s an apple” is not a true statement, because there are plenty of other fruits apart from apples.