Questions: Question 1 of 25 possible This question: 1 point(s) possible Write the statement in the form 'if p, then q'. No rational numbers are irrational Choose the statement that best rewrites the sentence in the specified form. A. If a number is rational, then it is sometimes irrational. B. If a number is rational, then it is never irrational. C. If a number is irrational, then it is sometimes rational.

Question 1 of 25 possible This question: 1 point(s) possible Write the statement in the form 'if p, then q'. No rational numbers are irrational Choose the statement that best rewrites the sentence in the specified form. A. If a number is rational, then it is sometimes irrational. B. If a number is rational, then it is never irrational. C. If a number is irrational, then it is sometimes rational.
Transcript text: Question 1 of 25 possible This question: 1 point(s) possible Write the statement in the form 'if $p$, then $q$. No rational numbers are irrational Choose the statement that best rewrites the sentence in the specified form. A. If a number is rational, then it is sometimes irrational. B. If a number is rational, then it is never irrational. C. If a number is irrational, then it is sometimes rational.
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Solution

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Solution Steps

Step 1: Identify the premise (p) and conclusion (q)

The premise is that the number is of type 'rational', and the conclusion is that the number is of type 'irrational'.

Step 2: Translate the relationship

Based on the relationship 'no', the translated statement is: If a number is rational, then it is never irrational.

Step 3: Apply logical negation where necessary

The translation incorporates logical negation based on the relationship type.

Step 4: Consider the nature of the sets

The translation considers the hierarchical and exclusive nature of the sets of numbers involved.

Final Answer: If a number is rational, then it is never irrational.

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