What is the contra positive statement of, ‘If the weather is cold, then there is snowing’ ?
If there is no snow then the weather is not cold
A conditional statement has the form if p then q. Its contrapositive is if not q then not p: the two parts are swapped and both are negated. The contrapositive is logically equivalent to the original statement, so it is always true whenever the original is true. Here p is the weather is cold and q is there is snowing.
Working:
Original: p → q (if the weather is cold, then there is snow)
Contrapositive: not q → not p
not q = there is no snow
not p = the weather is not cold
Contrapositive: if there is no snow then the weather is not cold
If there is snow, then the weather is cold is the converse (q → p), which only swaps the parts. If the weather is not cold then there is no snow is the inverse (not p → not q), which only negates the parts. If the weather is cold then there is no snow (p → not q) contradicts the original statement. None of these is equivalent to the original.
Hence, If there is no snow then the weather is not cold.
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