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allsm [11]
3 years ago
14

Rewrite the two statements as a single biconditional statement: A rectangle is a quadrilateral that has all perpendicular sides.

If all sides of a quadrilateral are perpendicular, then it is a rectangle.
Your friend claims that only true conditional statements have a true contrapositive. is your friend correct? explain your reasoning
Mathematics
1 answer:
Serjik [45]3 years ago
5 0

A) The single biconditional statement of the given statement is;

A quadrilateral is a rectangle if and only if it has all perpendicular sides

B) The statement made by your friend about only true conditional statements having a true contrapositive is; True

A biconditional statement is one that combines 2 conditional statements that are related to one another. An example of a biconditional statement is;

The polygon has only four sides if and only if the polygon is a quadrilateral.

That biconditional statement has combined two individual conditional statements.

Now, to our question, we are given two statements;

Statement 1; A rectangle is a quadrilateral that has all perpendicular sides.

Statement 2; If all sides of a quadrilateral are perpendicular, then it is a rectangle.

Combining both statements means that the biconditional statement will be; A quadrilateral is a rectangle if and only if it has all perpendicular sides

B) A contrapositive is when we switch and negate the hypothesis and the conclusion of a conditional statement. For example, the contrapositive of "If it is raining then the grass is wet" is "If the grass is not wet then it is not raining."

Thus, if the conditional statement is true, then we will have a true contrapositive.

Read more about contrapositives at; brainly.com/question/12276922

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