Suppose the Variable X Represents Students, Y Represents Courses, and T(x

question 68

Short Answer

suppose the variable x represents students, y represents courses, and T(x, y) means "x is taking y." $$\begin{array}{l}\text { Match the English statement with all its equivalent symbolic statements in this list: }\\\begin{aligned}1 . & \exists x \forall y T ( x , y ) & 2 . & \exists y \forall x T ( x , y ) & 3 . & \forall x \exists y T ( x , y ) \\4 . & \neg \exists x \exists y T ( x , y ) & 5 . & \exists x \forall y \neg T ( x , y ) & 6 . & \forall y \exists x T ( x , y ) \\7 . & \exists y \forall x \neg T ( x , y ) & 8 . & \neg \forall x \exists y T ( x , y ) & 9 . & \neg \exists y \forall x T ( x , y ) \\10 . & \neg \forall x \exists y \neg T ( x , y ) & 11 . & \neg \forall x \neg \forall y \neg T ( x , y ) & 12 . & \forall x \exists y \neg T ( x , y )\end{aligned}\end{array}$$
-Some courses are being taken by no students.

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Definitions:

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