Consider the following statements. p : If 3^4 > 4^3 , then 3^3 > 4^4 q : The roots of the equation x^2 - 2x + 2 = 0 are real if and only if Mumbai is in Maharashtra. r : Statement p is true or statement q is false. Which of the following has truth value T (true)?

Step-by-step solution

Evaluate the truth value of statement p : 3^4 = 81 and 4^3 = 64 , so 3^4 > 4^3 is True (T). 3^3 = 27 and 4^4 = 256 , so 3^3 > 4^4 is False (F). Statement p is of the form T F , which is False. Thus, p F . Evaluate the truth value of statement q : The discriminant of x^2 - 2x + 2 = 0 is D = 4 - 8 = -4 "Mumbai is in Maharashtra" is True (T). Statement q is of the form F T , which is False. Thus, q F . Evaluate the truth value of statement r : "Statement p is true" is False (since p F ). "Statement q is false" is True