Quiznetik
Essentials of the Symbolic Logic | Set 2
1. An ‘existential quantifier’ is symbolized as ,
A. ‘ ∃x’
B. ‘(x)’
C. ‘ x’
D. ( ∃x )
Correct : D. ( ∃x )
2. ‘Everything is mortal ‘ is symbolized as …………
A. ( ∃x ) ̴m x
B. ( ∃x ) m x
C. (x) m x
D. (x) ̴m x
Correct : C. (x) m x
3. ‘ Something is mortal’ is symbolized as
A. (x) m x
B. ( ∃x ) ̴m x
C. (x) ̴m x
D. ( ∃x ) m x
Correct : D. ( ∃x ) m x
4. ‘ Nothing is mortal’ is symbolized as
A. (x) ̴m x
B. ( ∃x ) m x
C. ( ∃x ) ̴m x
D. (x) m x
Correct : A. (x) ̴m x
5. ‘Something is not mortal’ is symbolized as
A. (x) m x
B. ( ∃x ) ̴m x
C. ( ∃x ) m x
D. (x) ̴m x
Correct : B. ( ∃x ) ̴m x
6. The negation of (x) M x is logically equivalent to……………………………….
A. (x) ̴m x
B. ( ∃x ) m x
C. ( ∃x ) ̴m x
D. (x) m x
Correct : C. ( ∃x ) ̴m x
7. The negation of (x) ̴M x is logically equivalent to……………………………….
A. ( ∃x ) ̴m x
B. (x) ̴m x
C. (x) m x
D. ( ∃x ) m x
Correct : D. ( ∃x ) m x
8. The negation of ( ∃x) ̴M x is logically equivalent to ………………….
A. (x) m x
B. ( ∃x ) ̴m x
C. (x) ̴m x
D. ( ∃x ) m x
Correct : A. (x) m x
9. The negation of ( ∃x) M x is logically equivalent to ……………………….
A. ( ∃x ) ̴m x
B. (x) ̴m x
C. ( ∃x ) m x
D. (x) m x
Correct : B. (x) ̴m x
10. ‘ All fruits are ripe’ is symbolized as
A. ( ∃x ) ( f x . r x )
B. ( ∃x ) ( f x . ̴r x )
C. (x) ( f x Ͻ r x )
D. (x) ( f x Ͻ ̴r x )
Correct : C. (x) ( f x Ͻ r x )
11. ‘ No fruits are ripe ‘ is symbolized as
A. (x) ( f x Ͻ r x )
B. ( ∃x ) ( f x . ̴r x )
C. (x) ( f x Ͻ ̴r x )
D. ( ∃x ) ( f x . r x )
Correct : C. (x) ( f x Ͻ ̴r x )
12. ‘Some fruits are ripe’ is symbolized as
A. ( ∃x ) ( f x . ̴r x )
B. ( ∃x ) ( f x . r x )
C. (x) ( f x Ͻ ̴r x )
D. (x) ( f x Ͻ r x )
Correct : B. ( ∃x ) ( f x . r x )
13. ‘Some fruits are not ripe’ is symbolized as
A. (x) ( f x Ͻ r x )
B. (x) ( f x Ͻ ̴r x )
C. ( ∃x ) ( f x . r x )
D. ( ∃x ) ( f x . ̴r x )
Correct : D. ( ∃x ) ( f x . ̴r x )
14. As per modern interpretation of traditional subject-predicate propositions, A and O propositions are …………………..
A. contraries
B. sub-contraries
C. sub alterns
D. contradictories
Correct : D. contradictories
15. As per modern interpretation of traditional subject-predicate propositions, E and I propositions are ………………………………
A. contradictories
B. sub alterns
C. sub-contraries
D. contraries
Correct : A. contradictories
16. The universal quantification of a propositional function is true if and only if ……...
A. at least one substitution instance is true
B. all of it’s substitution instances are false
C. all of it’s substitution instances are true
D. it has both true and false substitution instances
Correct : C. all of it’s substitution instances are true
17. The relation between the general propositions (x) Mx and (∃x ) ̴Mx is ……………
A. contrary
B. contradiction
C. sub contrary
D. sub altern
Correct : B. contradiction
18. The relation between the general propositions (x) ̴Mx and (∃x ) Mx is ………..……
A. contradiction
B. sub contrary
C. sub altern
D. contrary
Correct : A. contradiction
19. The relation between the general propositions (x) Mx and (x) ̴Mx is ……..………
A. sub contrary
B. contradiction
C. sub altern
D. contrary
Correct : D. contrary
20. The relation between the general propositions (∃x ) Mx and (∃x ) ̴Mx is …………
A. contrary
B. sub altern
C. sub contrary
D. contradiction
Correct : C. sub contrary
21. If (x) Mx is true, then (x) ̴Mx is …………………
A. true
B. false
C. true or false
D. valid
Correct : B. false
22. If (x) Mx is true, then (∃x ) Mx is …………………..
A. false
B. true
C. valid
D. true or false
Correct : B. true
23. If (x) Mx is true, then (∃x ) ̴Mx is …………………………..
A. true or false
B. true
C. false
D. valid
Correct : C. false
24. If (x) Mx is false, then (x) ̴Mx is …………………
A. valid
B. true
C. true or false
D. false
Correct : C. true or false
25. If (x) Mx is false, then (∃x ) Mx is …………………..
A. true or false
B. false
C. valid
D. true
Correct : A. true or false
26. If (x) Mx is false, then (∃x ) ̴Mx is …………………………..
A. true
B. valid
C. false
D. true or false
Correct : A. true
27. If (x) ̴Mx is true, then (∃x) Mx is …………………
A. true or false
B. false
C. true
D. valid
Correct : B. false
28. If (x) ̴Mx is true, then (∃x ) ̴Mx is …………………
A. valid
B. true
C. true or false
D. false
Correct : B. true
29. If (x) ̴Mx is true, then (x) Mx is …………………
A. false
B. true or false
C. true
D. valid
Correct : A. false
30. If (x) ̴Mx is false, then (x) Mx is …………………
A. true or false
B. true
C. valid
D. false
Correct : A. true or false
31. If (x) ̴Mx is false, then (∃x) Mx is …………………
A. false
B. valid
C. true
D. true or false
Correct : C. true
32. If (x) ̴Mx is false, then (∃x ) ̴Mx is …………………
A. true or false
B. true
C. false
D. valid
Correct : A. true or false
33. If (∃x ) Mx is true, then (x) Mx is …………………
A. false
B. valid
C. true
D. true or false
Correct : D. true or false
34. If (∃x ) Mx is true, then (x) ̴Mx is …………………
A. valid
B. true or false
C. false
D. true
Correct : C. false
35. If (∃x ) Mx is true, then (∃x ) ̴Mx is …………………
A. true
B. false
C. true or false
D. valid
Correct : C. true or false
36. If (∃x ) Mx is false, then (x) Mx is …………………
A. true or false
B. valid
C. true
D. false
Correct : D. false
37. If (∃x ) Mx is false, then (x) ̴Mx is …………………
A. valid
B. false
C. true or false
D. true
Correct : D. true
38. If (∃x ) Mx is false, then (∃x ) ̴Mx is …………………
A. true
B. true or false
C. valid
D. false
Correct : A. true
39. If (∃x ) ̴Mx is true , then (x) Mx is …………………
A. false
B. true or false
C. valid
D. true
Correct : A. false
40. If (∃x ) ̴Mx is true , then (x) ̴Mx is …………………
A. true
B. false
C. true or false
D. valid
Correct : C. true or false
41. If (∃x ) ̴Mx is true, then (∃x ) Mx is …………………
A. valid
B. true or false
C. false
D. true
Correct : B. true or false
42. If (∃x ) ̴Mx is false, then (x) Mx is …………………
A. true
B. true or false
C. valid
D. false
Correct : A. true
43. If (∃x ) ̴Mx is false, then (x) ̴Mx is …………………
A. true
B. true
C. false
D. valid
Correct : C. false
44. If (∃x ) ̴Mx is false, then (∃x ) Mx is …………………
A. true
B. false
C. valid
D. true or false
Correct : A. true
45. If (x) ( H x Ͻ Mx ) is true, then (∃x ) ( H x . ̴Mx ) is …………………
A. true
B. true or false
C. false
D. valid
Correct : C. false
46. If (x) ( H x Ͻ Mx ) is false , then (∃x ) ( H x . ̴Mx ) is …………………………
A. valid
B. true
C. true or false
D. false
Correct : B. true
47. If (x) ( H x Ͻ ̴Mx) is true, then (∃x ) ( H x . Mx ) is……………………….
A. false
B. valid
C. true
D. true or false
Correct : A. false
48. If (x) ( H x Ͻ ̴Mx ) is false , then (∃x ) ( H x . Mx ) is ……………………….
A. true or false
B. false
C. valid
D. true
Correct : D. true
49. If (∃x ) ( H x . Mx ) is true, then (x) ( H x Ͻ ̴Mx ) is …………………
A. true
B. true or false
C. false
D. valid
Correct : C. false
50. If (∃x ) ( H x . Mx ) is false , then (x) ( H x Ͻ ̴Mx ) is …………………
A. valid
B. true
C. true or false
D. false
Correct : B. true
51. If (∃x ) ( H x . ̴Mx ) is true, then (x) ( H x Ͻ Mx ) is ………………..
A. false
B. valid
C. true
D. true or false
Correct : A. false
52. If (∃x ) ( H x . ̴Mx ) is false , then (x) ( H x Ͻ Mx ) is ………………..
A. valid
B. false
C. true or false
D. true
Correct : D. true