“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.
I agree, if and only if trips me up too and it doesn’t fit perfectly into this logic formula. A thing is only an apple if and only if it is a fruit makes sense if you read it in a common sense way.
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“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.
I agree, if and only if trips me up too and it doesn’t fit perfectly into this logic formula. A thing is only an apple if and only if it is a fruit makes sense if you read it in a common sense way.