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Which of the following is a counterexample for this conditional statement?

a) a rectangle with sides measuring 3.2 and 5.3
b) a rectangle with sides measuring 10 and 7
c) a rectangle with sides measuring 3.9 and 5.1
d) a rectangle with sides measuring 1.5 and 2.5

User Zuckjet
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Final answer:

Option (d), a rectangle with sides measuring 1.5 and 2.5 cm, serves as a counterexample to the conditional statement, showing that not all rectangles with a side less than 3 cm are also less than 2 cm wide.

Step-by-step explanation:

To determine a counterexample for a conditional statement, we must understand what the conditional statement is. A counterexample is a specific case that shows a conditional statement to be false. If the statement is 'All rectangles with sides less than 3 cm are also less than 2 cm wide,' we are looking for a rectangle with one side less than 3 cm but not less than 2 cm in width. This would disprove the statement.

Looking at the options provided:

  • a rectangle with sides measuring 3.2 and 5.3 (option a)
  • a rectangle with sides measuring 10 and 7 (option b)
  • a rectangle with sides measuring 3.9 and 5.1 (option c)
  • a rectangle with sides measuring 1.5 and 2.5 (option d)

Option (d) presents a rectangle where one side (1.5 cm) is less than 3 cm, and the width (2.5 cm) is also less than 3 cm but more than 2 cm. Therefore, option (d) serves as a proper counterexample to the conditional statement.

User DerLola
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