Question

Consider the following statements:
$p:2$ is a prime number
$q:\cos {30}^{\circ }=\frac{1}{2}$
$r:{\sec }^{2}x+{\tan }^{2}x=1$
$s:\sqrt{7}$ is an irrational number
$u:{\pi }^2$ is greater than $10$

Then which among the following contain only valid statements?

• A. $p\vee q,q\vee r,r\vee s,s\vee u$
• B. $p\vee q,q\wedge r,r\vee s,s\wedge u$
• C. $p\vee q,q\vee s,r\vee s,s\vee u$
• D. $p\wedge q,q\wedge s,r\wedge s,s\wedge u$

Answer 1

The correct option is C $p\vee q,q\vee s,r\vee s,s\vee u$

$p$ is true $\left(T\right)$
$q$ is false $\left(F\right)$
$r$ is false $\left(F\right)$
$s$ is true $\left(T\right)$
$u$ is false $\left(F\right)$

We know that, a statement is valid if it's truth value is TRUE.
Checking individually for all the given expressions we find that $p\vee q,q\vee s,r\vee s$ and $s\vee u$ are valid.