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Maths (commerce) MCQ

Mathematical Logic (p-1) · Maharashtra Board STD 12 Commerce / Arts (MSBSHSE - English Medium). 15 questions.

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MCQ

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15 questions · auto-graded multiple-choice test.

MCQ 11 Mark
Which of the following is always true?
  • A
    ~(p → q) ≡ ~q → ~p
  • B
    ~(p ∨ q) ≡ ~p ∨ ~q
  • ✓
    ~(p → q) ≡ p ∧ ~q
  • D
    ~(p ∧ q) ≡ ~p ∧ ~q
Answer
Correct option: C.
~(p → q) ≡ p ∧ ~q
(c) ~(p → q) ≡ p ∧ ~q
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MCQ 21 Mark
The statement (~p ∧ q) ∨ ~q is
  • A
    p ∨ q
  • B
    p ∧ q
  • C
    ~(p ∨ q)
  • ✓
    ~(p ∧ q)
Answer
Correct option: D.
~(p ∧ q)
~(p ∧ q)
Hint:
(~p ∧ q) ∨ ~q = (~p ∨ ~q) ∧ (q ∨ ~q)
= (~p ∨ ~q) ∧ t
= ~p ∨ ~q
= ~(p ∧ q)
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MCQ 31 Mark
The negation of the proposition ‘If 2 is prime, then 3 is odd’, is
  • A
    If 2 is not prime, then 3 is not odd
  • ✓
    2 is prime and 3 is not odd
  • C
    2 is not prime and 3 is odd
  • D
    If 2 is not prime, then 3 is odd
Answer
Correct option: B.
2 is prime and 3 is not odd
(b) 2 is prime and 3 is not odd
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MCQ 41 Mark
If p : He is intelligent.
q : He is strong.
Then, symbolic form of statement: ‘It is wrong that, he is intelligent or strong’ is
  • A
    ~p ∨ ~p
  • B
    ~(p ∧ q)
  • ✓
    ~(p ∨ q)
  • D
    p ∨ ~q
Answer
Correct option: C.
~(p ∨ q)
(c) ~(p ∨ q)
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MCQ 51 Mark
Consider the following three statements
p : 2 is an even number.
q : 2 is a prime number.
r : Sum of two prime numbers is always even.
Then, the symbolic statement (p ∧ q) → ~r means:
  • A
    2 is an even and prime number and the sum of two prime numbers is always even.
  • B
    2 is an even and prime number and the sum of two prime numbers is not always even.
  • ✓
    If 2 is an even and prime number, then the sum of two prime numbers is not always even.
  • D
    If 2 is an even and prime number, then the sum of two prime numbers is also even.
Answer
Correct option: C.
If 2 is an even and prime number, then the sum of two prime numbers is not always even.
(c) If 2 is an even and prime number, then the sum of two prime numbers is not always even.
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MCQ 61 Mark
The false statement in the following is:
  • A
    p ∧ (~p) is a contradiction
  • ✓
    (p → q) ↔ (~q → ~p) is a contradiction
  • C
    ~(~p) ↔ p is a tautology
  • D
    p ∨ (~p) ↔ p is a tautology.
Answer
Correct option: B.
(p → q) ↔ (~q → ~p) is a contradiction
(b) (p → q) ↔ (~q → ~p) is a contradiction
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MCQ 71 Mark
Let p ∧ (q ∨ r) = (p ∧ q) ∨ (p ∧ r). Then this law is known as
  • A
    Commutative law
  • B
    Associative law.
  • C
    De Morgan’s law
  • ✓
    Distributive law
Answer
Correct option: D.
Distributive law
(d) Distributive law
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MCQ 81 Mark
Which of the following is an open statement?
  • ✓
    x is a natural number
  • B
    Give me a glass of water
  • C
    Wish you best of luck
  • D
    Good morning to all
Answer
Correct option: A.
x is a natural number
(a) x is a natural number
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MCQ 91 Mark
If p is any statement, then (p ∨ ~p) is a
  • A
    contingency
  • B
    contradiction
  • ✓
    tautology
  • D
    none of them
Answer
Correct option: C.
tautology
(c) tautology
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MCQ 101 Mark
Negation of the statement ‘This is false or That is true’ is
  • A
    That is true or This is false
  • B
    That is true and This is false
  • ✓
    This is true and That is false
  • D
    That is false and That is true
Answer
Correct option: C.
This is true and That is false
(c) This is true and That is false
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MCQ 111 Mark
Conditional p → q is equivalent to
  • A
    p → ~q
  • ✓
    ~p ∨ q
  • C
    ~p → ~q
  • D
    p ∨ ~q
Answer
Correct option: B.
~p ∨ q
(b) ~p ∨ q
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MCQ 121 Mark
If p is the sentence ‘This statement is false’, then
  • A
    truth value of p is T
  • B
    truth value of p is F
  • C
    p is both true and false
  • ✓
    p is neither true nor false
Answer
Correct option: D.
p is neither true nor false
(d) p is neither true nor false
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MCQ 131 Mark
If p and q are two statements, then (p → q) ↔ (~q → ~p) is
  • A
    contradiction
  • ✓
    tautology
  • C
    neither nor (b)
  • D
    none of these
Answer
Correct option: B.
tautology
(b) tautology
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MCQ 141 Mark
~(p ∨ q) ∨ (~p ∧ q) is logically equivalent to
  • ✓
    ~p
  • B
    p
  • C
    q
  • D
    ~q
Answer
Correct option: A.
~p
(a) ~p
Hint:
~(p ∨ q) ∨ (~p ∧ q) ≡ (~p ∧ ~q) ∨ (~p ∧ q)
≡ ~p ∧ (~q ∨ q)
≡ ~p ∧ t
≡ ~p
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MCQ 151 Mark
Which of the following is not a statement?
  • A
    Smoking is injurious to health
  • B
    2 + 2 = 4
  • C
    2 is only even prime number
  • ✓
    Come here
Answer
Correct option: D.
Come here
(d) Come here
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