CIS 1910 Lecture Notes - Lecture 4: Digital Object Identifier, Free Variables And Bound Variables

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04 qua(cid:374)tified state(cid:373)e(cid:374)ts: the expression x p(x) has 0 free variables. True: the expression x p(cid:4666)x(cid:4667) v q(cid:4666)x(cid:4667) is a proposition. False: the expression x (cid:4666)p(cid:4666)x(cid:4667) v q(cid:4666)x(cid:4667)(cid:4667) has one free variable. False: the expression x p(x) v x q(x) is a proposition. For the following questions, the domain for the variable x is the set of all positive integers. We have the following predicates: p(x): x is even, q(x): x is divisible by 3. X (p(x) ^ q(x)) true x = 6: t. X (p(x) q(x)) false x = 6: f. Let the domain be the natural numbers: n = 0,1, 2, : ca(cid:374) (cid:449)e e(cid:454)p(cid:396)ess i(cid:374) p(cid:396)edi(cid:272)ate logi(cid:272) (cid:862)the(cid:396)e a(cid:396)e at least 2 numbers that are bigger than. 10(cid:863): p(x) : x is bigger than 10, x y (p(x) ^ p(y) ^ (x y) Let the do(cid:373)ai(cid:374) (cid:271)e the (cid:374)atu(cid:396)al (cid:374)u(cid:373)(cid:271)e(cid:396)s: n = (cid:1004),(cid:1005), (cid:1006), .

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