Let x,yEN (x,y are the elements of the Natural Numbers). Natural numbers are counting numbers: {1, 2, 3, ...}. P(x): x is divisible by 2; Q(x, y): 7x-2

(10) Let E denote the set of even integers, and O denote the set of odd integers. (a) Let P = "Every integer is either even or odd." Write P using logic symbols (and common notation for sets, like E, Z, N, Q etc).

STRICTLY HANDWRITTEN THEN BOX THE FINAL ANSWERS

Let P(a, b) and Q(a, b) be the open sentences defined by P(a, b) : a = b andQ(a, b) : a^2 − b^2 = 0, respectively, where the variables a and b can take any value in Z. Determine the truth value of the open sentence Q(a, b) ⇒ P(a, b) for each (a, b) ∈ {(2, −2),(5, 7),(3, 3)}. Explain your answers.  (Z is the set of intergers)