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Venn Diagram Solution to Question Number 7" width="200" height="175" />
One example below
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Note it is the same answer as number 7. They are equivalent statements.
“If a square, then a rectangle.” or “All squares are rectangles”
and
“If not a rectangle, not a square.” or “All non-rectangles are non-squares”
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The converse of a conditional statement is formed by flipping the order in which the hypothesis and conclusion appear. For example, the converse of the statement “If it is raining, then the ground is wet” is “If the ground is wet, then it is raining.”
The inverse of a conditional statement is formed by negating both the hypothesis and conclusion. For example, the inverse of the statement “If it is raining, then the ground is wet” is “If it is not raining, then the ground is not wet”
The contrapositive of a conditional statement is formed by negating both the hypothesis and conclusion and flipping the order in which they appear. For example, the contrapositive of the statement “If it is raining, then the ground is wet” is “If the ground is not wet, then it is not raining.”
A biconditional statement is a statement in the form “If and only if P, then Q,” which is equivalent to the statement “P if and only if Q.” This means that P and Q are either both true or both false. For example, the statement “If and only if it is raining, the ground is wet” is a biconditional statement.
In geometry class, students learn about conditional statements and their related concepts (inverse, converse, contrapositive, and biconditional) in order to make logical deductions about geometric figures and their properties. These concepts are often used to prove theorems and solve problems.
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