Let I (x) be the statement "x has an Internet connection"and C(x, y) be the statement "x and y have chatted overthe Internet," where the domain for the variables x and yconsists of all students in your class. Use quantifiers toexpress "There is a student in your class who has chattedwith everyone in your class over the Internet."AaXvy C(x, y)В3Xay(x = y ^ vz ¬(C(x, z) ^ C(y, z)))эхзу(х %3D у л vz(C(x, z) v C(у, z)))D) aXvy(x = y I(y))

The statement is There is a student in your class who has chatted with everyone in your class over…

Answered: Let I (x) be the statement "x has an…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let P(x, y) be "x has taken class y," and Q(x, y) be "x has passed class y" and M(y) be "y is a math class," where the domain of x consists of all students in your class and the domain of y consists of all classes at LU. Use quantifiers to express this statement. (Assume that all email messages that were sent are received.) Every student in your class has passed a class at Liberty University that is not a math class.
Let M(x, y) be the statement "x is a role model for y," where the domain for both x and y consists of all people in the world. Use quantifiers to express "Someone is a role model for all people."* O 3xayM(x,y) O vx3yM(x,y) O None of the mentioned O 3XVYM(x,y) O VXVYM(xy)
Check if the following statement is TRUE or FALSE. Let p(x) and g(x) be two open predicates in a universe of discourse. Is it true that (x) (p(x) v g(x)) is equivalent to (Vxp(x)) v (Vxq(x))? O True O False
Show by example that these three statements are generally false:(a) A and AT have the same nullspace.(b) A and AT have the same free variables.(c) If R is the reduced form rref(A) then RT is rref(AT ).
axayP(x, y) is true when P(x, y) is false for every pair x, y. A True False
Use the rules of inference to show that if 3x(M(x) AP(x)) and Vx(K (x) → ¬M(x)) are true, then 3x(P(x) ^ ¬K(x)) is also true, where the domains of all the quantifiers are the same.
Select the description that characterizes the Boolean expression:
Discrete Math
8. Give an example of a predicate P(x) and different domains so that the state- ments VxP(x) is true, VxP(x) is false, xP(x) is true, xP(x) is false.
Let w(2) = In(2) (principal argument). Let X be the real axis (straight line). Then O w(X) is two circles O w(X) is a circle O w(X) is more than two vertical lines O w(X) is a horizontal line O w(X) is two rays O w(X) is a vertical line O w(X) is a ray O w(X) is two horizontal lines O w(X) is two vertical lines O w(X) is more than two horizontal lines O None of the other options is true

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