Discussion
Read these six conditional claims :
1. If it's an apple, then it's a fruit.
2. If it's a fruit, then it's an apple.
3. It's an apple if it's a fruit.
4. It's a fruit if it's an apple.
5. It's not a fruit if it's not an apple.
6. It's not an apple if it's not a fruit.
Out of these six conditional claims which three claims have the answer as Yes ?
Answer: D
The three true claims are 1, 4, 6.
Every apple is a fruit, but not every fruit is an apple. So any claim equivalent to ‘if apple, then fruit’ is true, and any claim equivalent to ‘if fruit, then apple’ is false.
- Claim 1 says if apple, then fruit: true.
- Claim 4, ‘fruit if apple’, says the same thing: true.
- Claim 6, ‘not an apple if not a fruit’, is the contrapositive of claim 1: true.
- Claims 2 and 3 both say if fruit, then apple: false. Claim 5, ‘not a fruit if not an apple’, is the contrapositive of that false claim, so it is false too.
Every other option includes at least one of claims 2, 3 or 5.
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