Consider the following statements p: 2 is an even prime number q : If z ₁=2-i, z ₂=-2+i where i= -1 , then Im [ 1 z₁ z ₂ ]=- 1 5 r: (-945^ )=-1 then which of the following has truth value True.

Step-by-step solution

Statement evaluation: Statement p : "2 is an even prime number" is True since 2 is the only even prime number. Statement q : With z₁ = 2-i and z₂ = -2+i , we find z₁ z ₂ = (2-i)(-2-i) = -4 - i^2 = -5 since i^2 = -1 . Then 1 z₁ z ₂ = - 1 5 , and Im [- 1 5 ] = 0 . The claim that Im [ 1 z₁ z ₂ ] = - 1 5 is false, so q is False . Statement r : Using (-945^ ) = - (945^ ) = - (5 180^ + 45^ ) = - (45^ ) = -1 , so r is True . Truth table: p = T , q = F , r = T Evaluating the options: A : (p q) (q r) = (T F) (F T) = F F = T