Oxirgi raqami juft son yoki 0 soni bilan tugaydigan sonlar ikkiga qoldiqsiz bo’linadi

1. 
   “Oxirgi raqami juft son yoki 0 soni bilan tugaydigan sonlar ikkiga qoldiqsiz bo’linadi.”- mulohazaning mulohazaviy formulasini ko’rsating.
   

1. 
   (A
   
2. 
   (A
   
3. 
   (A
   
4. 
   (A
   

2. 
   “Agar kamayuvchi va ayriluvchi sonlar ma’lum bir songa bo’linsa, ayirma ham shu songa bo’linadi.”- mulohazaning mulohazaviy formulasini ko’rsating.
   

1. 
   A
   
2. 
   A
   
3. 
   A
   
4. 
   A
   

3. 
   “Faqat o’ziga va birga bo’linadigan natural sonlarga tub sonlar deyiladi.”- mulohazaning mulohazaviy formulasini ko’rsating.
   

1. 
   (A
   
2. 
   (A
   
3. 
   (A
   
4. 
   A
   

4. 
   R (x): “x-tub son”
   

Q(x): “x-biror sonning kubi” predikatlari berilgan bo’lsin. X=1, 4, 8 qiymatlarni qabul qilsa, quyidagilardan qaysi biri faqat rost qiymatga ega bo’ladi?

1. 
   ⎤R (1), ⎤R (8), R (1) ∨Q (1), R(1)⇒Q(1), R (8) ∨Q (8), R(8)⇒Q(8)
   
2. 
   ⎤R (1), ⎤R (8), R (1) ∧Q (1), R(1)⇔Q(1), R (8) ∧Q (8), R(8)⇔Q(8)
   
3. 
   ⎤R (1), ⎤R (8), R (1) ∧Q (1), R(1)⇒Q(1), R (8) ∨Q (8), R(8)⇒Q(8)
   
4. 
   ⎤R (1), ⎤R (4), R (1) ∨Q (4), R(1)⇒Q(1), R (8) ∨Q (4), R(8)⇒Q(8)
   

5. 
   R (x): “x-tub son”
   

Q(x): “x-biror sonning kubi” predikatlari berilgan bo’lsin. X=1, 4, 8 qiymatlarni qabul qilsa, quyidagilardan qaysi biri faqat yolg’on qiymatga ega bo’ladi?

1. 
   ⎤R (1), ⎤R (8), R (1) ∧Q (1), R(1)⇔Q(1), R (8) ∧Q (8), R(8)⇔Q(8)
   
2. 
   ⎤R (1), ⎤R (8), R (1) ∧Q (1), R(1)⇒Q(1), R (8) ∨Q (8), R(8)⇒Q(8)
   
3. 
   ⎤R (1), ⎤R (4), R (1) ∨Q (4), R(1)⇒Q(1), R (8) ∨Q (4), R(8)⇒Q(8)
   
4. 
   ⎤R (1), ⎤R (8), R (1) ∨Q (1), R(1)⇒Q(1), R (8) ∨Q (8), R(8)⇒Q(8)
   

6. 
   R (x): “x-juft son” va x∈N bo’lsa, ∀x R(x) ni mulohazaga aylantiring.
   

1. 
   Ixtiyoriy x natural son juft sondir.
   
2. 
   Shunday x natural son topiladiki, ular juft son bo’ladi.
   
3. 
   Ixtiyoriy x natural son juft son emas.
   
4. 
   Ixtiyoriy x natural son juft son bo’ladi yoki bo’lmaydi/
   

7. 
   R(x, y): “” (∀x,y∈N) predikatni kvantorlardan foydalanib, rost mulohazaga aylantiring.
   

1. 
   ∀x, ∃y )
   
2. 
   ∀x, ∃y )
   
3. 
   ∀x, ∀y )
   
4. 
   ∃x, ∃y )
   

8. 
   R(x, y): “” (∀x,y∈N) predikatni kvantorlardan foydalanib, yolg’on mulohazaga aylantiring.
   

1. 
   ∀x, ∀y )
   
2. 
   ∀x, ∃y )
   
3. 
   ∀x, ∃y )
   
4. 
   ∃x, ∃y )
   

9. 
   R(x, y): “ (∀x,y∈N) bo’lsa, ∃x, ∀y ) mulohazaga aylantiring va qirmatini aniqlang.
   

1. 
   Shunday natural sonlarning kvadrati mavjudki, unga ixtiyoriy natural sonni qo’shsak, yig’indi 25dan kata bo’ladi.-1
   
2. 
   Ixtiyoriy natural sonlarning kvadrati mavjudki, unga ixtiyoriy natural sonni qo’shsak, yig’indi 25dan kata bo’ladi.-0
   
3. 
   Shunday natural sonlarning kvadrati mavjudki, unga shunday natural sonni qo’shsak, yig’indi 25dan kata bo’ladi.-0
   
4. 
   Ixtiyoriy natural sonlarning kvadrati mavjudki, unga shunday natural sonni qo’shsak, yig’indi 25dan kata bo’ladi.-1
   

10. 
    R(x): “”, x∈Z va Q(y): predikatlar berilgan. Quydagilarning qaysi biri faqat rost qiymat qabul qiladi.
    

1. 
   ∃x(⎤R(x)), ∀y Q(y)
   
2. 
   ∃x(⎤R(x)), ∃y(⎤Q(y))
   
3. 
   ∃x(⎤R(x)), ∀y Q(y)
   
4. 
   ∀x R(x), ∃y(⎤Q(y))