Consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the…

Consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code: Assertion (A) = Three rational numbers between $\frac{2}{3}$ and $\frac{3}{5}$ are $\frac{9}{20}$, $\frac{10}{20}$, and $\frac{11}{20}$. Reason (R) - A rational number between two rational numbers $p$ and $q$ is $\frac{1}{2}(p+q)$. The correct answer is:

  1. Both Assertion (A) and Reason (R) are true but Reason is not a correct explanation of Assertion (A).

  2. Assertion (A) is false and Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

  4. Assertion (A) is true and Reason (R) is false.

Solution

Solution:

 

We know that \(\frac{1}{2}(\text{p}+\text{q})\) is a rational number between two given rational numbers p and q. Thus, Reason (R) is true.

A rational number between \(\frac{2}{5}\) and \(\frac{3}{5}\) is \(\frac{1}{2}\Big(\frac{2}{5}+\frac{3}{5}\Big)=\frac{5}{10}\)

A rational number between \(\frac{2}{5}\) and \(\frac{5}{10}\) is \(\frac{1}{2}\Big(\frac{2}{5}+\frac{5}{10}\Big)=\frac{9}{20}\)

A rational number between \(\frac{5}{10}\) and \(\frac{3}{5}\) is \(\frac{1}{2}\Big(\frac{5}{10}+\frac{3}{5}\Big)=\frac{11}{20}\)

\(\therefore\) Three rational numbers between \(\frac{2}{5}\) and \(\frac{3}{5}\) are \(\frac{9}{20},\frac{10}{20}\) and \(\frac{11}{20}\)

Thus, Assertion (A) is true

Since Reason (R) gives Assertion (A), so (a) holds.

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