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ghari112345
05.12.2019 •
Mathematics
What are the converse, inverse, and contrapositive of the following true conditional? what are the truth values of each?
if a statement is false, give a counterexample.
if a figure is a rectangle, then it is a parallelogram.
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Ответ:
For the given statement, 'If a figure is a rectangle, then it is a parallelogram.' the converse is 'if a figure is a parallelogram, then it is rectangle.'
As can be seen, the converse statement is not true, hence the truth value of the converse statement is false.
The inverse of a conditional statement is the result of negating both the hypothesis and conclusion of the conditional statement. For example, the inverse of P → Q is ~P → ~Q.
For the given statement, 'If a figure is a rectangle, then it is a parallelogram.' the inverse is 'if a figure is not a rectangle, then it is not a parallelogram.'
As can be seen, the inverse statement is not true, hence the truth value of the inverse statement is false.
The contrapositive of a conditional statement is switching the hypothesis and conclusion of the conditional statement and negating both. For example, the contrapositive of P → Q is ~Q → ~P.
For the given statement, 'If a figure is a rectangle, then it is a parallelogram.' the contrapositive is 'if a figure is not a parallelogram, then it is not a rectangle.'
As can be seen, the contrapositive statement is true, hence the truth value of the contrapositive statement is true.
Ответ:
How rich is anthony
Step-by-step explanation: