Which statement is logically equivalent to the following conditional statement? "If it has exactly four sides, then it is not a hexagon."

Question

Which statement is logically equivalent to the following conditional statement?

"If it has exactly four sides, then it is not a hexagon."

1. If it does not have exactly four sides, then it is not a hexagon.
2. If it does not have exactly four sides, then it is a hexagon.
3. If it is a hexagon, then it does not have exactly four sides.
4. If it is not a hexagon, then it has exactly four sides.

Answer 1

For any given statement "If A, then B", the contrapositive statement, by definition "If not B, then not A", is logically equivalent to the original statement.

For this case, A="It has exactly four sides", and B="it is not a hexagon".

The contrapositive is "If it is not not a hexagon, then it does not have exactly four sides", which is equivalent to "If it is a hexagon, the it does not have exactly four sides". --> Answer choice 3

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