Formalized Symbolic Logics


FOPL

Q. Translate the following statements to FOPL: (Dec. 02)
  1. All employees earning more than Rs. 60,000 per year, pay income tax.
  2. No employee of a university earns more than the vice-chancellor.
  3. European vegetarian do not take milk, but Indian vegetarians do.

1. We define:
E(x) for x is an employee
GE(u, v) for u is greater than v
T(x) for x pays taxes

FOPL statement
" x(E(x) & GE(i(x), 60,000)) à T(x)

2. We define:
E(x) for x is an employee
C(y) for y is vice-chancellor
GE(u, v) for u is greater than v

FOPL statement
" xy((E(x) & C(y)) à GE(i(x), i(y)))

3. We define:
E(x) for x is a vegetarian
M(x) for x takes milk.

FOPL statement
" x((E(x: European) & E(x: Indian)) à (~M(x: European) & M(x: Indian)))

Q. Translate the following statements to FOPL:
  1. All men are mortal.
  2. Every orange is yellow.
  3. Any integer is either positive or negative.
  4. Some men are clever.
  5. Some real numbers are integers.

We define:

H(x) for x is a man
M(x) for x is mortal
O(x) for x is orange
Y(x) for x is yellow
C(x) for x is clever

N(x) for x is an integer
P(x) for x is either positive or negative

I(x) for x is an integer
R(x) for x is a real number

  1. " x (H(x) à M(x))
  2. " x (O(x) à Y(x))
  3. " x (N(x) à Y(x))
  4. $ x (H(x) à C(x))
  5. $ x (R(x) à I(x))
 
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