Answer:
Each understudy on the respect roll got an A.
No understudy who got a confinement got an A.
No understudy who got a confinement is on the respect roll.
No understudy who got an A missed class.
No understudy who got a confinement got an A.
No understudy who got a confinement missed class
Explanation:
M(x): x missed class
An (x): x got an A.
D(x): x got a confinement.
¬∃x (A(x) ∧ M(x))
¬∃x (D(x) ∧ A(x))
∴ ¬∃x (D(x) ∧ M(x))
The conflict isn't considerable. Consider a class that includes a lone understudy named Frank. If M(Frank) = D(Frank) = T and A(Frank) = F, by then the hypotheses are overall evident and the end is counterfeit. Toward the day's end, Frank got a control, missed class, and didn't get an A.
Each understudy who missed class got a confinement.
Penelope is an understudy in the class.
Penelope got a confinement.
Penelope missed class.
M(x): x missed class
S(x): x is an understudy in the class.
D(x): x got a confinement.
Each understudy who missed class got a confinement.
Penelope is an understudy in the class.
Penelope didn't miss class.
Penelope didn't get imprisonment.
M(x): x missed class
S(x): x is an understudy in the class.
D(x): x got imprisonment.
Each understudy who missed class or got imprisonment didn't get an A.
Penelope is an understudy in the class.
Penelope got an A.
Penelope didn't get repression.
M(x): x missed class
S(x): x is an understudy in the class.
D(x): x got a repression.
An (ax): x got an A.
H(x): x is on the regard roll
An (x): x got an A.
D(x): x got a repression.
∀x (H(x) → A(x)) a
¬∃x (D(x) ∧ A(x))
∴ ¬∃x (D(x) ∧ H(x))
Real.
1. ∀x (H(x) → A(x)) Hypothesis
2. c is a self-self-assured element Element definition
3. H(c) → A(c) Universal dispatch, 1, 2
4. ¬∃x (D(x) ∧ A(x)) Hypothesis
5. ∀x ¬(D(x) ∧ A(x)) De Morgan's law, 4
6. ¬(D(c) ∧ A(c)) Universal dispatch, 2, 5
7. ¬D(c) ∨ ¬A(c) De Morgan's law, 6
8. ¬A(c) ∨ ¬D(c) Commutative law, 7
9. ¬H(c) ∨ A(c) Conditional character, 3
10. A(c) ∨ ¬H(c) Commutative law, 9
11. ¬D(c) ∨ ¬H(c) Resolution, 8, 10
12. ¬(D(c) ∧ H(c)) De Morgan's law, 11
13. ∀x ¬(D(x) ∧ H(x)) Universal hypothesis, 2, 12
14. ¬∃x (D(x) ∧ H(x)) De Morgan's law, 13
