QuestionIs it true or false that every positive number is a positive irrational number? Choose A, B, C, or D.
Studdy Solution
STEP 1
Assumptions1. We understand the definition of a positive number A positive number is a number that is greater than zero. . We understand the definition of an irrational number An irrational number is a number that cannot be expressed as a simple fraction. It's decimal representation neither ends nor becomes periodic.
STEP 2
We need to evaluate the statement Every positive number is a positive irrational number.
STEP 3
We can disprove this statement by providing a counterexample. A counterexample is a specific case or example that contradicts a statement or proposition.
STEP 4
Consider the number2.. It is a positive number.
STEP 5
Check if2.5 is an irrational number. An irrational number cannot be expressed as a simple fraction, but2.5 can be expressed as the fraction5/2.
STEP 6
Since2.5 is a positive number and it is not an irrational number, it serves as a counterexample to the statement "Every positive number is a positive irrational number."
STEP 7
Therefore, the statement "Every positive number is a positive irrational number" is false.
The correct answer is B. False, because2.5 is a positive number but it is not an irrational number.
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