Exam 1: A: the Foundations: Logic and Proofs

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suppose the variable x represents students, y represents courses, and T(x, y) means "x is taking y." Match the English statement with all its equivalent symbolic statements in this list: 1. \existsx\forallyT(x,y) 2. \existsy\forallxT(x,y) 3. \forallx\existsyT(x,y) 4. \neg\existsx\existsyT(x,y) 5. \existsx\forally\negT(x,y) 6. \forally\existsxT(x,y) 7. \existsy\forallx\negT(x,y) 8. \neg\forallx\existsyT(x,y) 9. \neg\existsy\forallxT(x,y) 10. \neg\forallx\existsy\negT(x,y) 11. \neg\forallx\neg\forally\negT(x,y) 12. \forallx\existsy\negT(x,y) -Every course is being taken by at least one student.

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