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{"ops":[{"insert":"Let p and q be propositions\n\np: 4 is a rational number\nq: \u221a3 is an irrational number\n\nLet P(x) denote the statement  \"x \u2265 10.\" what are the truth values\n\nP(9)"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"P(12)"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"P(-10)"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"P(10)"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"P(0)"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"\nLet P(x) be the statement \"x has develop a program in JAVA\", where the domain for x consist of all student. write a statement in English corresponding to the for\n\n?x  P(x)"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"?x ~P(x)"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"?x  P(x) "},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"~?x  P(x)"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"~? ?x P(x)"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"\nLet P(x) denote the sentence 2x + y = 5. What are the truth values of the following where the domain of x and y is the set of all integers.\n\n?x ?y P( x,y)"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"?x ?y P( x,y)"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"?x ?y P( x,y)"},{"attributes":{"list":"ordered"},"insert":"\n"},{"insert":"?x ?y P( x,y)"},{"attributes":{"list":"ordered"},"insert":"\n"}]}

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