2 6 Points In af Match the English statement with all its e

(2) (6 Points) : In (a)-(f) Match the English statement with all its equivalent symbolic statements in this list: 1·3xVy T(x, y) 3. Vx3y T(x, y) 4Th3, T(x, y) 5 xVy-T(x, y) 6. vy3x T(x, y) 7. 3yVx-T(x, y) a) Some student is taking every course. b) There is a course that all students are taking c) Every student is taking at least one course. d) No course is being taken by all students e) No student is taking any course f) Some students are taking no courses

Solution

(2).

x-> student y->course

a). Some student is taking every course

ans 1. x (S(x) y ( C(y) T(x,y)))

b). There is a course that all student are taking

ans 2. y (C(y) x ( S(x)) T(x,y))

c). Every student is taking atleast one subject

ans 3. x ( S(x) y ( C(y) T(x,y)))

d). No course is being taken by all students

ans 8. ¬ y (C(y) x ( S(x)) T(x,y))

e). No student is taking any course

ans 4. ¬ x (S(x) y ( C(y) T(x,y)))

f). Some student are taking no courses

ans 5. x (S(x) y ( C(y) ¬ T(x,y)))