Consider the three statements - p : n N , 10 n -3 is a prime number, when n is not divisible by 3 . q : 2 3 , -2 3 , -1 3 are the direction cosines of a directed line. r : x is an increasing function in the interval [ - 2 , 2 ] . Then which of the following statement pattern has truth value true?

Step-by-step solution

Statement p : For n = 8 0 3 , we compute 10 8 - 3 = 77 = 7 11 , which is not prime. This counterexample shows p is false. Statement q : Verify ( 2 3 )^2 + ( -2 3 )^2 + ( -1 3 )^2 = 4 3 + 4 3 + 1 3 = 3 1 , so these cannot be direction cosines. Statement q is false. Statement r : The derivative d dx ( x) = x 0 on [- 2 , 2 ] , and strictly positive on the open interval, confirming that x is increasing. Statement r is true. Truth values: p = F, q = F, r = T. A : (p q) r = ( F F ) T = F T = F B : (p q) r = ( F F ) F = T