Question

For any two real numbers $\theta$ $\varphi$, we define $\theta R\varphi$ if and only if ${\sec }^2\theta -{\tan }^2\varphi =1$. The relation $R$ is

• A. Reflexive but not transitive
• B. Symmetric but not reflexive
• C. Both reflexive and symmetric but not transitive
• D. An equivalence relation

Answer 1

Answer: (C)

Both reflexive and symmetric but not transitive

Given ,$\theta$ R$\varphi$ where $\theta$ and $\varphi$ are two real numbers.

${\sec }^2\theta -{\tan }^2\varphi =1$

$\theta =\varphi$

R is reflexive and symmetric.

R is not transitive since there are only two numbers.