Write the negation of the following:
Every rectangle with four equal sides is a square.
A) No rectangle with four equal sides is not a square.
B) Every square with four equal sides is not a rectangle.
C) Every rectangle with four equal sides is not a square.
D) No square with four equal sides is a rectangle.
I think the answer is B
All squares are rectangles, but not all rectangles are squares. Although they should not be using a double-negative, A means the same as "A rectangle with four equal sides is a square."
To find the negation of a statement, we typically add "not" or "it is not the case that" to the original statement. In this case, the original statement is "Every rectangle with four equal sides is a square."
Let's examine each option:
A) "No rectangle with four equal sides is not a square."
This option adds a double negative, which can be confusing. It is better to use a single negative. Therefore, this option is incorrect.
B) "Every square with four equal sides is not a rectangle."
This option negates the original statement, correctly stating that not every square with four equal sides is a rectangle. Hence, this option is correct.
C) "Every rectangle with four equal sides is not a square."
This option messes up the negation since it is the same as the original statement. Hence, this option is incorrect.
D) "No square with four equal sides is a rectangle."
This option negates the original statement, correctly stating that no square with four equal sides is a rectangle. Therefore, this option is also correct.
In this instance, both options B and D give the correct negation of the original statement.