Concept explainers
To find: the converse, inverse, and contrapositive of the given statement.
Answer to Problem 50PPS
Theconverse and inverse of the statement is false and contrapositive is true.
Explanation of Solution
Given information:
The statement is given “All squares are rectangles”.
Find the converse of the given statement.
Converse of the statement is “if a shape is rectangle, then it is a square”.
Which is false.
Counterexample:
A shape with length 5 and breadth 3 is a rectangle but could not be a square.
Find the inverse of the statement.
The inverse of the statement is “if a shape is not a square, then it is not a rectangle”
Which is the false.
Counterexample:
A shape with length 5 and breadth 3 is a rectangle but could not be a square.
Find the contrapositive of the statement.
The contrapositive of the statement is “if a shape is not a rectangle, then it is not a square”
Which is true.
Therefore, the converse and inverse of the statement is false and contrapositive is true.
Chapter 2 Solutions
Geometry, Student Edition
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