JUST DO (e) 34 Chapter 1. Logie Exercise 9. Suppose the universe of discoarse is

Question

JUST DO (e)

34 Chapter 1. Logie Exercise 9. Suppose the universe of discoarse is the set of people Allen. Betty, Chuck). To save writing sometimes we shall write a for Allen,&for; Betty, and c for Chack. Let P(r, u) be the seetence "x l Suppose the truth value of P(r, p) depends on r and y as shown in the following table. Note that in this table, z refers to the rows and y refers to the columns. For instance, P(c,b) is true and P(b, c) is false. (a) Is the sentence (y)P(a. y) true or false What does the sentence (w)P(a, v) mean in ordi- nary English? Answer the same two questions about each of the two sentences ()P/b, y) and 0%) Pic, p), Make a table showing how the truth value of the sentence (Yy)P(z, y) depends on z. What does the sentence (Vy)P(x, v) mean? (b) Is the sentence (B)(y)Pa.u) true or false? What does this sentence mean in ordinary English? (c) Make a table showing how the truth value of the sentence (Br)P(z, y) depends on y. What does (d) (e) the sestence (Bx)P(z, y) mean? Is the sentence (u)Br) P(z. y) true or false? What does this sentence mean in ordinary English? Consider the two conditional sentences and Which of these two sentences is true and which is false in this example? Which of the variables z and y is free in the sentence P(z, y)? Answer the same question about each of the four sentences (Vg)P(.). (Br)()P.), (Br)P(r,y), and ()ar)P,). (f)

Explanation / Answer

Part (e) The first conditional sentence is true and the second is false.

This is because if for some x , all y are true then for all y there will be at least 1 x which will be true

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