Question

Let
$p:2$ 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 statements are valid

• 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 $p\vee q,q\vee s,r\vee s,s\vee u$

$\text{p is true (T)}$
$\text{q is false (F)}$
$\text{r is false (F)}$
$\text{s is true (T)}$
$\text{u is false (F)}$

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